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Re: In the figure above, if z = 50, then x + y = [#permalink]
18 Jun 2013, 22:50

My 30 second solution:

sum of angles in triangle = 180

Sum of angles in small triangle: (180-y) + (180-x) + 90 = 180 --> x+y = 270

IMO the information z = 50 is not needed to calculate x+y if we know that the two vertical lines are parallel and hence we have a right angle in the smaller triangle. Let me know if my reasoning is wrong.

Re: In the figure above, if z = 50, then x + y = [#permalink]
19 Jun 2013, 01:18

1

This post received KUDOS

Expert's post

kingflo wrote:

My 30 second solution:

sum of angles in triangle = 180

Sum of angles in small triangle: (180-y) + (180-x) + 90 = 180 --> x+y = 270

IMO the information z = 50 is not needed to calculate x+y if we know that the two vertical lines are parallel and hence we have a right angle in the smaller triangle. Let me know if my reasoning is wrong.

Cheers

An exterior angle of a triangle ( In this case y) is always equal to the sum of the opposite interior angles [ In this case 90 degrees and (180-x)]

Re: In the figure above, if z = 50, then x + y = [#permalink]
29 Nov 2013, 12:17

Expert's post

Yes, the setup of y = 90 + (180 - x)

is a great way to solve this question without knowing x or y.

If you are not familiar with spotting exterior angles and prefer to do things the old school way - well, there's plenty of information in the diagram from which you can gather together to find the actual value of y. And then from there you can solve for x and then add up x and y.

Either method works fine.

Below is a video demonstration of the adding up x and y approach: