Find the measure of the three angles in a triangle, if the measure of second angle is twice the first and the third angle is 20 degrees fewer than the first.

Question

THANK YOU!

Answer 1

Angles are:

First angle:

A

Second angle B

Third angle C

The measure of second angle is twice the first means:

B = 2 A

The third angle is 20° fewer than the first means:

C = A - 20°

The sum of angles in a triangle is 180°

A + B + C = 180°

A + 2 A + A - 20° = 180°

4 A - 20° = 180°

Add 20° to both sides

4 A = 200°

A = 200° / 4 = 50°

Now:

B = 2 A = 2 ∙ 50° = 100°

C = A - 20° = 50° - 20° = 30°

Three angles in this triangle are:

50° , 100° , 30°