Sally drew a circle with right triangle PRQ inscribed in it, as shown below: The figure shows a circle with points P, Q, and R o
n it forming an inscribed triangle. Side PQ is a chord through the center and angle R is a right angle. Arc QR measures 40 degrees. If the measure of arc QR is 40°, what is the measure of angle PQR? 20° 40° 50° 70°
Side PQ is a chord through the center and angle R is a right angle. This means that side PQ is the diameter of the circle.
Let O represent the center of the circle.
If the measure of arc QR is 40°, it means that the central angle formed by arc QR is 40°. Side OR and side OQ are equal because they are both radius of the circle. Therefore, ∆QOR is an isosceles triangle and the base angles are equal.
Therefore, ∠PQR = ∠ORQ
Since the sum of the angles in a triangle is 180°, then
Because you just turn -0.875 into a decimal: To convert a fraction to a decimal, divide the numerator by the denominator. If required, you can use a calculator to do this.