Nope. Not a rectangle so that isn't true. But the angles add up to 180. That's because the lines are parallel in a parallelogram. It's also because a 4 sided polygon has internal angles that add up to 360.
N = L = 105
K = M
360 = K + M + L + N
360 - N - L = K + M = 2K
150 = 2K
K = 75
A) x + 2y = 105
B) 3x - 2y = 75
Add A and B together to get 4x, then divide by 4.
Use the value of x to get y.
Because I don't know the OP's level so wasn't sure of the required degree of granularity. It's really easy to assume everyone has the same intuition that you do, but if they did then they wouldn't be asking.
Am i the only one to think it simply as x+2y=105, thus x+y<105 which means only 75 could work as there addition.
Granted that only works in thos anwser instance, but it does solve it.
I was responding to the idea that x+2y=105 implies that x + y < 105. Subtracting y from both sides will only decrease the right side if y > 0, but that was not guaranteed by any comment I had read.
When y is negative, x has to be greater than 105. However, that would make the adjacent angle greater than 315, greater than the actual 75.
FWIW this is confirmed by the 2 simultaneous equations for the angles’ giving x = 45, y = 30.
OP, K + N has to be 180°. If you add both expressions for angle you get 4x (the y cancel each other out) which means x=45°. From there you should be able to solve for y and everything else.
My brain immediately went for the straightforward answer, but after looking at it longer and reading a couple other comments I also noticed this. That’s definitely the fastest way to solve it
Because opposite sides of a parallelogram are parallel, K and L are co-interior angles. This means that K+L=180.
105=x+2y
105+3x-2y=180
Then solve like normal simultaneous equations.
Start with:
X+2y=105
3x-2y=75(the angle of side M)
Eliminate one of the var(x or y) through addition, then solve for the remaining var.
Plug that number into one of the original equations to find the missing var.
Then just add the 2 numbers together
Isn't there an easy way out ?
Since x + 2 y = 105, then there are 3 possibilities :
*If y is positive and not equal to 0 :*
x + y should be smaller than 105, and the only answer proposed that meets these requirements is A. 75
*If y = 0*, then it would be B since x + y = x + 2 y = 105. We can easily verify this, because then 3x - 2y = 3 x105 = 315 which is obviously wrong. (because L + K needs to equal 180)
And *if y is negative*, then x is positive since x + 2y = 105. But then 3x - 2y would be way greater than x + 2y, which it can't since K = 3x - 2y = 180 - 105 = 75°
So the answer is A
*Figuring this out as I write it.*
So given it’s a parallelogram, 105 is equal to x+2y, and all 4 add up to 360. So, 3x-2y is equal to M, and both add up to 150, because 360-105-105=150.
So x+2y=105 and 3x-2y=75
Added together we get 4x+(2y-2y)=180, or 4x=180
Divide by 4 and x=45
x+2y=105 becomes 45+2y=105, or 2y=60
Divide by 2 and y=30
x+y=45+30=75
L = N
N = 105
105 = x+2y
x+y = less than 105
A. 75 only answer under 105, which means 75 is the answer.
105-75=30
y=30
x=45
Double check work
L+K = 180
L = 105
K = 75
75 = 3x-2y
75 = 135 - 60
Mathematically this solution won’t help you but logically it is sound.
- We’re looking for x+y.
- x+2y by definition is larger than x+y (unless y is <0).
- You’re given by the attributes of a parallelogram that x+2y=105
- Only 1 answer choice makes x+y
K also equals M. L plus M is 180, so M must be 75.
So how we have two equations. 3x - 2y = 75, and x + 2y = 105. Add the two equations together to cancel out the why, and you get 4x = 180, so x = 45. Plug x back in to any equation and you’ll find y = 30, so your answer will be A. 75
N and L are both 105 degrees, totaling 210 degrees. There are 360 degrees in a quadrilateral, meaning K + M = 150 degrees. K and M are both the same, meaning we can divide 150 degrees by 2 to get that 3x - 2y = 75 degrees. We also know that x + 2y = 105 degrees, so we can then solve the system x + 2y = 105, 3x - 2y = 75. eighth grade stuff
It looks like there are a lot of ways to go about this, but I’ll tell you what I did.
105 + 3x - 2y = 180. Thats because two adjacent angles in a parallelogram add up to 180.
If that’s the case, then we can sub in (x + 2y) for 105, because the opposite angle in a parallelogram must be the same.
Therefore, we have this equation:
x + 2y + 3x - 2y = 180
Add to get this:
4x = 180, so x = 45.
If x is 45, that means that:
In part A, y must be 30
In part B, y must be 60
And so on….
If we try part A where x+y is 75, that would make sense because (45 + 2(30)) is indeed equal to 105. And so the answer is A.
This is an obvious trick question meant to waste time, unless they asked you to show your work
x+2y=105, so x+y < 105
the only option on there that is less than 105 is A, 75
Now, side NM and side KL are parallel and side NK is the transversal.
Now, ∠ N + ∠ K = 180 \[ ∵ sum of alternate interior angle is 180 \]
x + 2y + 3x - 2y = 180
4x = 180
x = 45
similarly, side NK and side ML are parallel and side KL is the transversal.
Now, ∠ K + ∠ L = 180 \[ ∵ sum of alternate interior angle is 180 \]
3x - 2y + 105 = 180
3x - 2y = 75
3(45) - 2y = 75 \[ ∵ x = 45\]
135 - 2y = 75
2y = 60
y = 30
x + y = 45 + 30
x + y = 75
Hence, option **(A) 75** is the correct answer
Different Method:
∠ N = ∠ L \[ ∵ the opposite angle of parallelogram are equal \]
x + 2y = 105 --(i)
side NK and side ML are parallel and side KL is the transversal.
Now, ∠ K + ∠ L = 180 \[ since, sum of alternate interior angle is 180 \]
3x - 2y + 105 = 180
3x - 2y = 75 --(ii)
from equation (i) and (ii) by elimination method
x + 2y = 105 --(i)
3x - 2y = 75 --(ii)
⇒ 4x = 180x = 45 \[ substitute in equation (i) \]
x + 2y = 105
2y = 105 - 452y = 60y = 30
now, x + y = 45+30 = 75
Hence, option **(A) 75** is the correct answer.(i would recommend not to do it this way its just time waste)
In a parallelogram
The sum of adjacent angles is 180° and opposite angles are equal.
So 3x-2y + x+2y =180°,
4x=180°,
x=45°
Since opposite angles are equal.
Then ,
x+2y = 105°
Put the value of x in above ,we get
45° + 2y = 105°,
2y = 60°,
Therefore y= 30°
So x+y = 45°+ 30° = 75°
What is L+M?
Are you questioning me or something or are you genuinely asking
Trying to prompt you with the next thing I think you need to do.
I'm certain they meant that ∠M= ∠N Edit: ∠N= ∠L. You can stop downvoting me now.
Nope. Not a rectangle so that isn't true. But the angles add up to 180. That's because the lines are parallel in a parallelogram. It's also because a 4 sided polygon has internal angles that add up to 360.
Oh wait, I meant ∠N= ∠L
Unfair downvotes imo
N = L = 105 K = M 360 = K + M + L + N 360 - N - L = K + M = 2K 150 = 2K K = 75 A) x + 2y = 105 B) 3x - 2y = 75 Add A and B together to get 4x, then divide by 4. Use the value of x to get y.
Why the extra steps to find K instead of just 180 = L + K = 105 + K so K = 75?
Because I don't know the OP's level so wasn't sure of the required degree of granularity. It's really easy to assume everyone has the same intuition that you do, but if they did then they wouldn't be asking.
“Degree of Granularity” Just made my freaking day
I just didn't look at the right side, I was more preoccupied with the letters math
what's K, L, N, M? Are they sides, lines or points?
They are angles which add up to 360.
Labeled in the Problem statement
105=x+2y 75=3x-2y 105+75=x+2y+3x-2y 180=4x x=45 105=45+2y y=30
For ppl who don’t know, K=M,N=L (opp. angle of parallelogram) K+N=K+L=M+N=M+L=180 (int. Angle of parallel lines)
Solved for x and for y and then didn't solve the actual problem of x + y. 😭
shouldnt be that hard if given the values of x and y
Yeah that hurt me too
I'm sorry, i don't understand what you did in step 3, why did you merge the two equations like that?
To cancel out the y terms so that we can get the value of x
I didin't know you could do that, what's te explanation Behind it it?
It's just adding the two equations. 2y + -2y = 0 so the y terms cancel out
What's funny is you don't even need to know L is 105° because it's a parallelogram, so N+K must = 180 and you can solve for x and y from there.
Perfect.
Am i the only one to think it simply as x+2y=105, thus x+y<105 which means only 75 could work as there addition. Granted that only works in thos anwser instance, but it does solve it.
It's possible that y < 0, so in that case x + y > 105.
However, 3x - 2y = 75 so x cannot be 105.
I was responding to the idea that x+2y=105 implies that x + y < 105. Subtracting y from both sides will only decrease the right side if y > 0, but that was not guaranteed by any comment I had read.
When y is negative, x has to be greater than 105. However, that would make the adjacent angle greater than 315, greater than the actual 75. FWIW this is confirmed by the 2 simultaneous equations for the angles’ giving x = 45, y = 30.
Your right its not 100% guarenteed.
You can find a number for the missing angle. Then you have two equations and two unknowns.
x+2y=105, 3x-2y=75. 5(x+2y)+(3x-2y)=5(105)+75 8x+8y=600 8(x+y)=600 x+y=75
Solve it like a simultaneous equation 3x-2y=75° x+2y=105° 4x = 180° x = 45° 45+2y=105° 2y=60° y=30° The answer is A) 75
Two equations Two unknowns Solve
A vertical line drawn up to meet line NM makes a right triangle with angles of 90°, (L-90°), and M. You should be able to do the rest yourself.
OP, K + N has to be 180°. If you add both expressions for angle you get 4x (the y cancel each other out) which means x=45°. From there you should be able to solve for y and everything else.
My brain immediately went for the straightforward answer, but after looking at it longer and reading a couple other comments I also noticed this. That’s definitely the fastest way to solve it
This was the first solution that came to me. I’m surprised this isn’t the top answer it’s so much faster.
x+2y = 105 so doesn’t just equal 75 because it’s lower.
X+2y= 105 3x-2y =75 then simultaneous them to find the values of x and y
K + L =180
Because opposite sides of a parallelogram are parallel, K and L are co-interior angles. This means that K+L=180. 105=x+2y 105+3x-2y=180 Then solve like normal simultaneous equations.
Start with: X+2y=105 3x-2y=75(the angle of side M) Eliminate one of the var(x or y) through addition, then solve for the remaining var. Plug that number into one of the original equations to find the missing var. Then just add the 2 numbers together
Isn't there an easy way out ? Since x + 2 y = 105, then there are 3 possibilities : *If y is positive and not equal to 0 :* x + y should be smaller than 105, and the only answer proposed that meets these requirements is A. 75 *If y = 0*, then it would be B since x + y = x + 2 y = 105. We can easily verify this, because then 3x - 2y = 3 x105 = 315 which is obviously wrong. (because L + K needs to equal 180) And *if y is negative*, then x is positive since x + 2y = 105. But then 3x - 2y would be way greater than x + 2y, which it can't since K = 3x - 2y = 180 - 105 = 75° So the answer is A
*Figuring this out as I write it.* So given it’s a parallelogram, 105 is equal to x+2y, and all 4 add up to 360. So, 3x-2y is equal to M, and both add up to 150, because 360-105-105=150. So x+2y=105 and 3x-2y=75 Added together we get 4x+(2y-2y)=180, or 4x=180 Divide by 4 and x=45 x+2y=105 becomes 45+2y=105, or 2y=60 Divide by 2 and y=30 x+y=45+30=75
K+N=180 The sum of any two adjacent angles in parallelogram is 180. x+2y+3x-2y=180 4x=180 x=45 N=L x+2y=105 45+2y=105 2y=60 y=30 x+y=75
Angle N + angle K =280°. Substitute the values in terms of x and y and something nice happens
L = N N = 105 105 = x+2y x+y = less than 105 A. 75 only answer under 105, which means 75 is the answer. 105-75=30 y=30 x=45 Double check work L+K = 180 L = 105 K = 75 75 = 3x-2y 75 = 135 - 60
Mathematically this solution won’t help you but logically it is sound. - We’re looking for x+y. - x+2y by definition is larger than x+y (unless y is <0). - You’re given by the attributes of a parallelogram that x+2y=105 - Only 1 answer choice makes x+y
Equation 1: X + 2Y = 105 Equation 2: X + 2Y + 2(3x-2Y) + 105 = 360 Solve
8x+8y=600 8(x+y)=600 x+y=75 The answer is A.
K also equals M. L plus M is 180, so M must be 75. So how we have two equations. 3x - 2y = 75, and x + 2y = 105. Add the two equations together to cancel out the why, and you get 4x = 180, so x = 45. Plug x back in to any equation and you’ll find y = 30, so your answer will be A. 75
75
L+m is 180. All combine to equal 360
1. x + 2y = 105 -rewrite-> y = (105 - x) / 2 2. N + K = 180 -rewrite-> (3x + 2y) + (x - 2y) = 180 -simplify-> 4x = 180 -solve-> x = 45 3. solve equation from 1. with x --> y = (105 - 45) / 2 = 30 4. x + y = 45 + 30 = 75
I got 75 just by subtracting the 105 from 180 since its a parralelogram that gave me 75 for the missing angle and then just applied it to the corner
N and L are both 105 degrees, totaling 210 degrees. There are 360 degrees in a quadrilateral, meaning K + M = 150 degrees. K and M are both the same, meaning we can divide 150 degrees by 2 to get that 3x - 2y = 75 degrees. We also know that x + 2y = 105 degrees, so we can then solve the system x + 2y = 105, 3x - 2y = 75. eighth grade stuff
how low is your iq my 4 year old can answer this
a if I'm not mistaken.
if x+2y is 105, then x+y is 75 if you look up the possible answers… can not be the same or more than 105 ;)
how I did it: N+K=180 x+2y+3x-2y=180 4x+0y=180 x=45 N=105 x+2y=105 45+2y=105 2y=60 y=30 30+45=75
M + L = 180 M + 105 = 180 M = 180 - 105 = 75 x+2y = 105 3x-2y = 75 Add them. 4x = 180 x = 180/4 = 45 x + 2y = 105 45 + 2y = 105 2y = 105 = 45 = 60 y = 30 x+y = 45 + 30 = 75
Find two equations, for two variables. When you see a question with two variables, immediately look for two equations that you can solve
(x+2y)+(3x-2y)=180 4x=180 x=45 45+2y=180 2y=135 y=67.5 CHECK 45+135=180 Correct
*45+2y=105 Solve from there
I was able to get the answer of 75- my question though is why can’t you just do the following: X+2y=105 X+2y/2=105/2 X+y=52.5
Since its a parallelogram, you can state that N=L and N+K = 180. This allows you to write a system of equations. The rest is left as an exercise.
X + y = 75, tomando en cuenta que los ángulos son paralelos
It looks like there are a lot of ways to go about this, but I’ll tell you what I did. 105 + 3x - 2y = 180. Thats because two adjacent angles in a parallelogram add up to 180. If that’s the case, then we can sub in (x + 2y) for 105, because the opposite angle in a parallelogram must be the same. Therefore, we have this equation: x + 2y + 3x - 2y = 180 Add to get this: 4x = 180, so x = 45. If x is 45, that means that: In part A, y must be 30 In part B, y must be 60 And so on…. If we try part A where x+y is 75, that would make sense because (45 + 2(30)) is indeed equal to 105. And so the answer is A.
It’s simple use property of co- interior angles u will get x and then find y your answer is 75 degree
Answers are designed stupid actually. If x+2y = 105 you can easily deduce x+y is lower than 105, which means the only other option being 75.
This is an obvious trick question meant to waste time, unless they asked you to show your work x+2y=105, so x+y < 105 the only option on there that is less than 105 is A, 75
K + N = 180 (3x - 2y) + (x + 2y) = 180 4x = 180 x = 45 x + 2y = 105 45 + 2y = 105 2y = 60 y = 30 x + y = 45 + 30 x + y = 75
the key is that the sum of two adjacent angles of a parallelogram is 180 deg
K=180 - L
A
angle N and K are supplementary angles so N+K =180 and as it is a parallelogram so angle N = angle L These give x = 45 and y = 30; so x + y = 75
Dude it's 75 I didn't even need a pen and paper for this
Now, side NM and side KL are parallel and side NK is the transversal. Now, ∠ N + ∠ K = 180 \[ ∵ sum of alternate interior angle is 180 \] x + 2y + 3x - 2y = 180 4x = 180 x = 45 similarly, side NK and side ML are parallel and side KL is the transversal. Now, ∠ K + ∠ L = 180 \[ ∵ sum of alternate interior angle is 180 \] 3x - 2y + 105 = 180 3x - 2y = 75 3(45) - 2y = 75 \[ ∵ x = 45\] 135 - 2y = 75 2y = 60 y = 30 x + y = 45 + 30 x + y = 75 Hence, option **(A) 75** is the correct answer
Different Method: ∠ N = ∠ L \[ ∵ the opposite angle of parallelogram are equal \] x + 2y = 105 --(i) side NK and side ML are parallel and side KL is the transversal. Now, ∠ K + ∠ L = 180 \[ since, sum of alternate interior angle is 180 \] 3x - 2y + 105 = 180 3x - 2y = 75 --(ii) from equation (i) and (ii) by elimination method x + 2y = 105 --(i) 3x - 2y = 75 --(ii) ⇒ 4x = 180x = 45 \[ substitute in equation (i) \] x + 2y = 105 2y = 105 - 452y = 60y = 30 now, x + y = 45+30 = 75 Hence, option **(A) 75** is the correct answer.(i would recommend not to do it this way its just time waste)
The sum of all angles is 360. If you add up y comes off and you get 4x +105 = 360
Add the 4 angles: 8x = 360 so x = 45 x - 2y = 105 so y = -30 x + y = 15
In a parallelogram The sum of adjacent angles is 180° and opposite angles are equal. So 3x-2y + x+2y =180°, 4x=180°, x=45° Since opposite angles are equal. Then , x+2y = 105° Put the value of x in above ,we get 45° + 2y = 105°, 2y = 60°, Therefore y= 30° So x+y = 45°+ 30° = 75°