Question

11/7 - isosceles and equilateral practice
6 of 2
possible points: 0.8
find the unknown angle measures.

m∠b = degrees
m∠c = degrees

Explanation:

Step1: Use the property of isosceles triangle

In an isosceles triangle, if two sides are equal (here \(AC = BC\)), then the angles opposite those sides are equal. So \(\angle A=\angle B = 66^{\circ}\).

Step2: Use the triangle - angle sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). Let \(\angle C=x\). Then \(\angle A+\angle B+\angle C = 180^{\circ}\). Substitute \(\angle A = 66^{\circ}\) and \(\angle B = 66^{\circ}\) into the equation: \(66^{\circ}+66^{\circ}+x=180^{\circ}\).

$$x=180^{\circ}-(66^{\circ} + 66^{\circ})=180^{\circ}-132^{\circ}=48^{\circ}$$

Answer:

\(m\angle B = 66\) degrees
\(m\angle C = 48\) degrees