Question

the measure of angle q, in the image provided, is 70 degrees. which of the following is the measure of angle p? a) 70^0 b) 40^0 c) 55^0 d) 80^0

Explanation:

Step1: Identify isosceles triangle

The markings on the sides of triangle \(PQR\) indicate that \(PR = PQ\), so \(\angle R=\angle Q = 70^{\circ}\).

Step2: Use angle - sum property of a triangle

The sum of interior angles of a triangle is \(180^{\circ}\). Let \(\angle P=x\). Then \(x + 70^{\circ}+70^{\circ}=180^{\circ}\).

Step3: Solve for \(\angle P\)

\[

$$\begin{align*} x&=180^{\circ}-(70^{\circ}+ 70^{\circ})\\ x&=180^{\circ}-140^{\circ}\\ x& = 40^{\circ} \end{align*}$$

\]

Answer:

B. \(40^{\circ}\)