# Evaluate the angle x in terms of angles and y and z?

I need help with this problem and problems like this. I know that to solve this problem I have to find which angles are the same and etc, but how do I know that. How can I see that two angles are the same or if their sum is a certain angle ?

For example like this problem:

In the following figure,AB ̅and ̅̅̅̅CD are parallel. Evaluate the angle x in terms of angles y and z.

How do I approach this problem ? Can you give me some tips for these types of problems ? I would really appreciate it.

• If AB and CD are parallel then that implies BD extended forms the same angle of intersection with them at both ends. The same goes for AC. Commented Jul 15, 2016 at 13:31
• Start by drawing it out, extending AB, AC and BD, and writing in the missing angles which are equal to others. you will also use 2 rules: sum of angles within a triangle is 180 degrees, and sum of angles on a straight line is 180 degrees. Commented Jul 15, 2016 at 13:32
• @RobertFrost So the y angle at point B is equal to the angle at point D ? Commented Jul 15, 2016 at 13:36
• Yes, the higher of the two angles by D. Commented Jul 15, 2016 at 13:41

$x=z+y$

If you extend AB, BD and AC you will se that the angle outside of B is $y$.

Since AB and DC are parallel, the internal angle next to D and inside the triangle with $z$ is equal to $y$.

The angle next to $x$ and inside the triangle with $z$ is therefore $180-(z+y)$

$x$ is therefore $z+y$.

• The moment you posted the question I figured it out hahaha. Thank you for the tips :D Commented Jul 15, 2016 at 13:42

Label angle $CDB$ as $y$ and use the exterior angle theorem for triangles in Euclidean geometry.