Question

in isosceles △srt, ∠r and ∠t are the base angles, and m∠s = 53°. what is the measure of each base angle?
a. 74°
b. 60.5°
c. 63.5°
d. 53°

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$. In $\triangle SRT$, let $m\angle R = m\angle T=x$ (since $\triangle SRT$ is isosceles and $\angle R$ and $\angle T$ are base - angles) and $m\angle S = 53^{\circ}$. So, $m\angle R+m\angle T + m\angle S=180^{\circ}$, which gives $x + x+53^{\circ}=180^{\circ}$.

Step2: Simplify the equation

Combining like terms, we get $2x+53^{\circ}=180^{\circ}$. Then, subtract $53^{\circ}$ from both sides: $2x=180^{\circ}- 53^{\circ}=127^{\circ}$.

Step3: Solve for $x$

Divide both sides of the equation $2x = 127^{\circ}$ by 2. So, $x=\frac{127^{\circ}}{2}=63.5^{\circ}$.

Answer:

C. $63.5^{\circ}$