Question

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

Explanation:

Step1: Identify the triangle type

The triangle has two equal - length sides (marked with the same tick marks), so it is an isosceles triangle. In an isosceles triangle, the angles opposite the equal sides are equal. So, \(m\angle B=m\angle C\).

Step2: Use the triangle - angle sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). Let \(m\angle B = m\angle C=x\). We know that \(m\angle A = 71^{\circ}\). Then, by the angle - sum formula \(m\angle A+m\angle B+m\angle C = 180^{\circ}\), we substitute the values: \(71^{\circ}+x + x=180^{\circ}\).

Step3: Solve the equation for \(x\)

Simplify the equation \(71^{\circ}+2x=180^{\circ}\). Subtract \(71^{\circ}\) from both sides: \(2x=180^{\circ}-71^{\circ}=109^{\circ}\). Then divide both sides by 2: \(x=\frac{109^{\circ}}{2}=54.5^{\circ}\).

Answer:

\(m\angle B = 54.5^{\circ}\), \(m\angle C = 54.5^{\circ}\)