Question

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


The figure shows a circle with points P, Q, and R on it forming an inscribed triangle. Side PQ is a chord through the center an


If the measure of arc QR is 100°, what is the measure of angle PQR? (6 points)

Answer 1

The value of  ∠PQR is 70 degree.

What is a Circle ?

A circle is a round figure whose all points lie in the same plane.

It is given that

The figure shows a circle with points P, Q, and R on it forming an inscribed triangle, measure of arc QR is 100°,

The measure of an inscribed angle is equal to one-half of the measure of the arc subtended by it,

Therefore

m∠QPR = (1/2) * 100° = 50°.

Angles in triangle

∠ PRQ = 90°

and ∠QPR =20°.

The value of the angle ∠PQR is

By angle sum property

90 +20+ x = 180

110 +x = 180

x = 70

Therefore the value of  ∠PQR is 70 degree.

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