Question

in triangle abc, the measure of angle a is 72°, the measure of angle b is 45°, what is the measure of angle c? a. 63° b. 27° c. 243° d. 117°

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$. So, $\angle A+\angle B+\angle C = 180^{\circ}$.

Step2: Substitute given angle values

We know that $\angle A = 72^{\circ}$ and $\angle B=45^{\circ}$. Substituting these values into the equation: $72^{\circ}+ 45^{\circ}+\angle C=180^{\circ}$.

Step3: Simplify the left - hand side

First, add $72^{\circ}$ and $45^{\circ}$: $72 + 45=117^{\circ}$, so the equation becomes $117^{\circ}+\angle C = 180^{\circ}$.

Step4: Solve for $\angle C$

Subtract $117^{\circ}$ from both sides of the equation: $\angle C=180^{\circ}-117^{\circ}=63^{\circ}$.

Answer:

A. $63^{\circ}$