Answer
The measure of angle A is 60 degrees.
The measure of angle B is 30 degrees.
The measure of angle C is 90 degrees.
Work Step by Step
Let x represent the measure of angle A.
The measure of angle C is one-half the measure of angle A.
One-half the measure of angle A means $\frac{1}{2}$ $\times$ x = $\frac{x}{2}$.
So, the measure of angle C is $\frac{x}{2}$.
The measure of angle B is 30 more than the measure of angle A.
30 more than the measure of angle A means 30 + x.
So, the measure of angle B is 30 + x.
The sum of the angles of every triangle equals 180 degrees.
So, we set up the following equation:
x + $\frac{x}{2}$ + 30 + x = 180
x + $\frac{x}{2}$ + x = 150
2x + $\frac{x}{2}$ = 150
Multiply both sides by 2:
4x + x = 300
5x = 300
Divide both sides by 5:
x = 60
The measure of angle A is 60 degrees.
The measure of angle B is $\frac{60}{2}$ = 30 degrees.
The measure of angle C is 30 + 60 = 90 degrees.
