Question

Gina drew a circle with right triangle PRQ inscribed in it as shown below.

Answer 1

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Based on the image attached above, the measure of angle PQR is letter D which is 50° as the half of 100° is 50. 

Answer 2

Answer:

The correct option is:  C) 40°

Step-by-step explanation:

The measure of arc $QR$ is $100\°$

So,  

$m\angle RPQ= \frac{1}{2}(m\widehat{QR})\\ \\ m\angle RPQ= \frac{1}{2}(100\°)\\ \\ m\angle RPQ=50\°$

Now, as $\triangle PRQ$ is right triangle, so $m\angle PRQ= 90\°$

Sum of all three angles in any triangle is always $180\°$

So,

$m\angle PQR \\ \\ = 180\°-(m\angle PRQ+m\angle RPQ)\\ \\ =180\°-(90\°+50\°)\\ \\ =180\°-140\°\\ \\ =40\°$

Thus, the measure of $\angle PQR$ is  $40\°$