# In triangle​ ABC, the size of angle B is 5 times the size of angle​ A, and the size of angle C is 18° less than 4 times the size of angle A?

Jan 14, 2018

$\angle A = {19.8}^{\circ}$, $\angle B = {99}^{\circ}$, and $\angle C = {61.2}^{\circ}$

#### Explanation:

Recall that the total sum of inner angles of a triangle is ${180}^{\circ}$.

Since $\angle B = 5 \angle A$ and $C = 4 \angle A - {18}^{\circ}$

Then we can say

${180}^{\circ} = \angle A + 5 \angle A + 4 \angle A - {18}^{\circ}$

Then we can simplify and get

${198}^{\circ} = 10 \angle A$

Then

$\angle A = {19.8}^{\circ}$

Then we plug in to get

$\angle B = {99}^{\circ}$

and

$\angle C = {61.2}^{\circ}$