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? (4 points)
(0 pts) 20°
(0 pts) 40°
(0 pts) 50°
(4 pts) 70°

Answer 1

I got this one right by guessing, but I wanted to know how to solve it.

Answer 2

measure of arc QR is 40 means QR subtends 40 degrees at the center
now theres a property of circles which states angle subtended at center by a chord is twice than at any other point on the circumference
which means QPR = 40/2 =20 degrees..
so req angle becomes 70 degress..was i clear enough ?

Answer 3

Yes! Thank you!

Answer 4

glad to help ^_^