### Third Angle Theorem

If two angles in one triangle are congruent to two angles in another triangle, then the third pair of angles must also congruent. This is called the **Third Angle Theorem**.

If

What if you were given

### Examples

#### Example 1

Determine the measure of all the angles in each triangle.

#### Example 2

Determine the measure of all the angles in each triangle.

#### Example 3

Determine the measure of the missing angles.

From the Third Angle Theorem, we know

#### Example 4

Explain why the Third Angle Theorem works.

The Third Angle Theorem is really like an extension of the Triangle Sum Theorem. Once you know two angles in a triangle, you automatically know the third because of the Triangle Sum Theorem. This means that if you have two triangles with two pairs of angles congruent between them, when you use the Triangle Sum Theorem on each triangle to come up with the third angle you will get the same answer both times. Therefore, the third pair of angles must also be congruent.

#### Example 5

Determine the measure of all the angles in the triangle:

First we can see that

### Review

Determine the measures of the unknown angles.

∠Y ∠x ∠N ∠L

∠E ∠F ∠H

You may assume that

∠ACB ∠HIJ ∠HJI ∠IHJ

∠RQS ∠SRQ ∠TSU ∠TUS

### Review (Answers)

To see the Review answers, open this PDF file and look for section 4.5.