Question

in the diagram below, \\( \angle pqr \\) is inscribed in circle \\( s \\) and \\( \overline{pr} \\) is a diameter. what is \\( m \angle qpr \\)?

Explanation:

Step1: Use the property of inscribed angle subtended by a diameter

An angle inscribed in a semicircle is a right angle. So, \(m\angle PQR = 90^{\circ}\).

Step2: Use the angle - sum property of a triangle

In \(\triangle PQR\), we know that the sum of the interior angles of a triangle is \(180^{\circ}\). Let \(m\angle QPR=x\). Then \(x + 65^{\circ}+90^{\circ}=180^{\circ}\).

$$x=180^{\circ}-(90^{\circ} + 65^{\circ})$$

$$x=180^{\circ}-155^{\circ}$$

Answer:

\(25\)