Question

the two triangles below are similar. also, ( mangle c = 15^{circ} ) and ( mangle b = 35^{circ} ) as shown below. find ( mangle p ), ( mangle q ), and ( mangle r ). assume the triangles are accurately drawn.

Explanation:

Step1: Find \(m\angle A\)

The sum of angles in a triangle is \(180^{\circ}\). For \(\triangle ABC\), \(m\angle A=180^{\circ}-m\angle B - m\angle C\). Substituting \(m\angle B = 35^{\circ}\) and \(m\angle C=15^{\circ}\), we get \(m\angle A=180^{\circ}-35^{\circ}-15^{\circ}=130^{\circ}\).

Step2: Use the property of similar triangles

Since \(\triangle ABC\sim\triangle QRP\) (by the order of vertices in similar triangles), corresponding angles are equal. So \(m\angle P=m\angle A = 130^{\circ}\), \(m\angle Q=m\angle B=35^{\circ}\), and \(m\angle R=m\angle C = 15^{\circ}\).

Answer:

\(m\angle P = 130^{\circ}\), \(m\angle Q=35^{\circ}\), \(m\angle R = 15^{\circ}\)