Question

In triangle ABC, the measure of the exterior angle at point B is 100°. If m∠A is 4 times larger than m∠c, FIND m∠c

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Answer 1

m<c = 20º

Explanation:

We use these following definitions:

The sum of an interior angle with its exterior is of 180º.

The sum of the three interval angles of a triangle is 180º.

The measure of the exterior angle at point B is 100°.

This means that the measure of the interior angle is: 180 - 100 = 80º

m∠A is 4 times larger than m∠c

This means that the measure of angle c is x, and the measure of angle a is 4x. The other angle, B, is 80º. So

`x + 4x + 80 = 180`

`5x = 100`

`x = (100)/(5)`

`x = 20`

The measure of angle C is 20º.