Question

1 in the diagram of $\triangle abc$ below, $\overline{ab} \cong \overline{ac}$. the measure of $\angle b$ is $40^\circ$.

Explanation:

(Assuming the question is to find the measure of ∠A or ∠C, let's solve for ∠A. Since \( \overline{AB} \cong \overline{AC} \), \( \triangle ABC \) is isosceles with \( \angle B \cong \angle C \).)

Step1: Identify isosceles triangle properties

In \( \triangle ABC \), \( AB \cong AC \), so \( \angle B = \angle C = 40^\circ \).

Step2: Use triangle angle sum theorem

The sum of angles in a triangle is \( 180^\circ \). Let \( \angle A = x \). Then \( x + 40^\circ + 40^\circ = 180^\circ \).

Step3: Solve for \( x \)

\( x = 180^\circ - 40^\circ - 40^\circ = 100^\circ \).

Answer:

The measure of \( \angle A \) is \( 100^\circ \) (or if finding \( \angle C \), it's \( 40^\circ \); adjust based on the actual question, but assuming finding \( \angle A \) here).