Question

refer to the given figure, which includes an isosceles triangle with ab = bc. if ∠bca measures 64°, what is the measure of ∠b? the measure of ∠b is °.

Explanation:

Step1: Use isosceles - triangle property

Since \(AB = BC\), \(\angle BAC=\angle BCA = 64^{\circ}\) in \(\triangle ABC\).

Step2: Apply angle - sum property of a triangle

The sum of interior angles of a triangle is \(180^{\circ}\). Let \(\angle B=x\). Then \(x + 64^{\circ}+64^{\circ}=180^{\circ}\).

Step3: Solve for \(\angle B\)

\(x=180^{\circ}-(64^{\circ}+64^{\circ})=180^{\circ}-128^{\circ}=52^{\circ}\).

Answer:

\(52\)