Question

Can anyone help and tell me the measure of all 20 angles? I'm struggling. Some of them I figured out, but I'm not 100% confident that they are correct. This is a Geometry problem.

Answer 1

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Explanation:

When two lines cross, the angles opposite each other are equal (they are called vertical angles--different from how we use the word vertical in other math classes) The angles next to each other add up to 180° (supplementary angles)

All the angles in a triangle add up to 180°

Perpendicular lines makes right angles, those are 90°

When you have parallel lines and another line crossing them, you get 8 angles, but 4 if them are all the same. Subtract the measure from 180 and you have the measure of the other four angles. Look for a Z shape; the angles tucked inside the Z are alternate interior angles and they are equal. The alternate interior angles and their vertical angles are what make up the 4-pack of equal angles.

These are all the rules you need to know to find all 20 of the angles in your question. See images