Question

the measure of angle q is 70 degrees. find the measure of angle p. type the answer in the box below. angle p has a measure of

Explanation:

Step1: Identify the triangle type

Since \(PR = PQ\), \(\triangle PRQ\) is an isosceles triangle. In an isosceles triangle, the base - angles are equal. So, \(\angle R=\angle Q = 70^{\circ}\).

Step2: Use the triangle - angle sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). Let \(\angle P=x\). Then \(x+\angle R+\angle Q = 180^{\circ}\). Substitute \(\angle R = 70^{\circ}\) and \(\angle Q = 70^{\circ}\) into the equation: \(x + 70^{\circ}+70^{\circ}=180^{\circ}\).

Step3: Solve for \(x\)

Simplify the left - hand side of the equation: \(x+140^{\circ}=180^{\circ}\). Subtract \(140^{\circ}\) from both sides: \(x=180^{\circ}-140^{\circ}\).

Answer:

\(40\)