Question

Sally drew a circle with the right triangle PRQ inscribed in it, as shown below: if the measure of arc QR is 40 degrees, what is the measure of angle PQR?
A) 20 degrees
B) 40 degrees
C) 50 degrees
D) 70 degrees

Answer 1

Answer:

D) 70 degrees

Step-by-step explanation:

Here,

Right triangle PRQ inscribed in a circle,

Let O be the centre of the circle,

If the measure of arc QR is 40 degrees,

By the central angle theorem,

$m\angle QPR = \frac{\widehat{QR}}{2}=\frac{40^{\circ}}{2}=20^{\circ}$,

Now, by the given options it is clear that measure of angle PQR can not 90°,

Thus, m∠PRQ = 90°,

∵ The sum of all interior angles of a triangle is supplementary,

m∠PRQ + m∠QPR + m∠PQR = 180°,

90° + 20° + m∠PQR = 180°,

110° + m∠PQR = 180°,

m∠PQR = 70°,

Hence, OPTION D would be correct.