Question

properties of isosceles triangles (diagram)
question
find ( mangle rqp ).

Explanation:

Step1: Use the property of isosceles triangles

In an isosceles triangle, if two sides are equal, then the angles opposite those sides are equal. Here, since \(PQ = RQ\), \(\angle P=\angle R = 26^{\circ}\).

Step2: Use the triangle - angle sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). Let \(\angle RQP=x\). Then, by the triangle - angle sum theorem \(x+\angle P+\angle R = 180^{\circ}\).
Substitute \(\angle P = 26^{\circ}\) and \(\angle R = 26^{\circ}\) into the equation: \(x+26^{\circ}+26^{\circ}=180^{\circ}\).
Simplify the left - hand side: \(x + 52^{\circ}=180^{\circ}\).
Solve for \(x\): \(x=180^{\circ}-52^{\circ}\).

Answer:

\(128\)