# Thread: Angle Congruent/Supplement Problem

1. ## Angle Congruent/Supplement Problem

Hello!

I have a geometry problem from the book "College Geometry: A Discovery's Approach" that is giving me a hard time. It is as follows:

Problem: 4.1 22
Prove that if two angles with respective sides are perpendicular, the angles are either congruent or a supplementary pair.

I managed to solve this problem a long time back but I forgot how to do it -_-.

Anyone who can solve this?

2. ## Re: Angle Congruent/Supplement Problem

Originally Posted by dauid
Hello!

I have a geometry problem from the book "College Geometry: A Discovery's Approach" that is giving me a hard time. It is as follows:

Problem: 4.1 22
Prove that if two angles with respective sides are perpendicular, the angles are either congruent or a supplementary pair.

I managed to solve this problem a long time back but I forgot how to do it -_-.

Anyone who can solve this?
1. Draw sketches.

2. In the 1st case you have a quadrilateral whose interior angles sum up to 360°. Since two of the angle sum up to 180° there are left 180° for the remaining two angles.

3. You have two right triangles with a common angle $\alpha$. Thus the remaining angles in the right triangles must be equal.