In triangle ABC, the measure of angle B is three times that of angle A. The measure of angle C is 20 degrees more than that of angle A. How do you find the angle measures?

Oct 28, 2016

$\angle A = {32}^{\circ}$
$\angle B = {96}^{\circ}$
$\angle C = {52}^{\circ}$

Explanation:

In a triangle, the three interior angles always add up to 180°:

Let $\angle A = x$
$\implies \angle B = 3 x$
$\implies \angle C = x + 20$

$\angle A + \angle B + \angle C = {180}^{\circ}$
$\implies x + 3 x + x + 20 = 180$
$\implies 5 x + 20 = 180$
$\implies 5 x = 160$
$x = 32$

Therefore, $\angle A = x = {32}^{\circ}$
$\angle B = 3 x = 3 \cdot 32 = {96}^{\circ}$
$\angle C = x + 20 = 32 + 20 = {52}^{\circ}$