Question

1 what is the measure of ∠b? a 56° b 73° c 34° d 146°

Explanation:

Step1: Identify triangle type

The marks on the sides of the triangle indicate it is an isosceles triangle. In an isosceles triangle, the base - angles are equal.

Step2: Recall angle - sum property

The sum of the interior angles of a triangle is 180°. Let $\angle B=\angle C = x$. We know $\angle A = 34^{\circ}$. So, $34^{\circ}+x + x=180^{\circ}$.

Step3: Solve for $x$

Combining like - terms, we get $34^{\circ}+2x = 180^{\circ}$. Subtract 34° from both sides: $2x=180^{\circ}- 34^{\circ}=146^{\circ}$. Then divide both sides by 2: $x=\frac{146^{\circ}}{2}=73^{\circ}$.

Answer:

B. $73^{\circ}$