Question

find the unknown angle measures.
m∠a=□°
m∠c=□°

Explanation:

Step1: Identify the triangle type

Since \(AB = AC\), \(\triangle ABC\) is an isosceles triangle. In an isosceles triangle, \(\angle B=\angle A\). Given \(\angle B = 65^{\circ}\), so \(m\angle A=65^{\circ}\).

Step2: Use the triangle - angle sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). Let \(m\angle A = 65^{\circ}\), \(m\angle B=65^{\circ}\), and \(m\angle C=x\). Then \(m\angle A + m\angle B+m\angle C=180^{\circ}\). Substitute the values: \(65^{\circ}+65^{\circ}+x = 180^{\circ}\).

Step3: Solve for \(x\)

\(x=180^{\circ}-(65^{\circ} + 65^{\circ})\).
\(x = 180^{\circ}-130^{\circ}\).
\(x = 50^{\circ}\), so \(m\angle C = 50^{\circ}\).

Answer:

\(m\angle A = 65^{\circ}\), \(m\angle C=50^{\circ}\)