Question

1. find the measure of ∠b in the triangle below if m∠a = m∠c.

Explanation:

Step1: Recall angle - sum property of a triangle

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

Step2: Substitute the given angle and the relationship

Since $m\angle A = m\angle C = 47^{\circ}$, we substitute these values into the angle - sum formula: $47^{\circ}+m\angle B + 47^{\circ}=180^{\circ}$.

Step3: Solve for $m\angle B$

First, simplify the left - hand side: $m\angle B+94^{\circ}=180^{\circ}$. Then, subtract $94^{\circ}$ from both sides: $m\angle B=180^{\circ}-94^{\circ}=86^{\circ}$.

Answer:

$86^{\circ}$