Question

m∠p =
m∠q =
m∠r =

Explanation:

Step1: Identify the triangle type

The triangle with all three sides equal (marked with the same tick marks) is an equilateral triangle.

Step2: Use the property of angles in an equilateral triangle

In an equilateral triangle, all angles are equal. The sum of angles in a triangle is \(180^{\circ}\). Let each angle be \(x\). Then \(x + x+ x=180^{\circ}\), i.e., \(3x = 180^{\circ}\).

Step3: Solve for \(x\)

Dividing both sides of \(3x = 180^{\circ}\) by \(3\), we get \(x=\frac{180^{\circ}}{3}=60^{\circ}\).

Answer:

\(m\angle P = 60^{\circ}\)
\(m\angle Q = 60^{\circ}\)
\(m\angle R = 60^{\circ}\)