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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.

enter image description here

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

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  • $\begingroup$ 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. $\endgroup$ Commented Jul 15, 2016 at 13:31
  • $\begingroup$ 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. $\endgroup$ Commented Jul 15, 2016 at 13:32
  • $\begingroup$ @RobertFrost So the y angle at point B is equal to the angle at point D ? $\endgroup$
    – Gigaxel
    Commented Jul 15, 2016 at 13:36
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    $\begingroup$ Yes, the higher of the two angles by D. $\endgroup$ Commented Jul 15, 2016 at 13:41

2 Answers 2

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$x=z+y$

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 $z+y$.

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    $\begingroup$ The moment you posted the question I figured it out hahaha. Thank you for the tips :D $\endgroup$
    – Gigaxel
    Commented Jul 15, 2016 at 13:42
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Label angle $CDB$ as $y$ and use the exterior angle theorem for triangles in Euclidean geometry.

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