Question

sally drew a circle with right triangle prq inscribed in it, as shown below: if the measure of arc qr is 40°, what is the measure of angle pqr? 20° 40° 50° 70°

Explanation:

Step1: Recall inscribed - angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc.

Step2: Identify the intercepted arc and inscribed angle

Angle $QPR$ is the inscribed angle that intercepts arc $QR$. Given arc $QR = 40^{\circ}$, so $\angle QPR=\frac{1}{2}\times40^{\circ}=20^{\circ}$.

Step3: Use the property of a right - triangle

Since $\triangle PRQ$ is a right - triangle with $\angle PRQ = 90^{\circ}$, and the sum of the interior angles of a triangle is $180^{\circ}$. Let $\angle PQR=x$. Then $\angle QPR+\angle PRQ+\angle PQR = 180^{\circ}$.

Step4: Solve for $\angle PQR$

Substitute the known values: $20^{\circ}+90^{\circ}+x = 180^{\circ}$. So $x=180^{\circ}-(20^{\circ}+90^{\circ}) = 70^{\circ}$.

Answer:

$70^{\circ}$