pr and qs are diameters of circle t. what is the measure of sr? 80° 100° 120° 50°
pr and qs are diameters of circle t. what is the measure of sr? 80° 100° 120° 50°
Answer
Explanation:
Step1: Recall inscribed - angle theorem
The measure of an inscribed angle is half the measure of its intercepted arc. In (\triangle PQT), (\angle PQT = 40^{\circ}), and (\angle PQT) is an inscribed angle that intercepts arc (PT). So the measure of arc (PT) is (2\times\angle PQT=80^{\circ}).
Step2: Use properties of a circle
Since (PR) is a diameter of circle (T), the measure of arc (PQR) is (180^{\circ}). Also, since (QS) is a diameter, the circle is symmetric about (QS). The measure of arc (PR = 180^{\circ}). We know that arc (PR=\text{arc }PT+\text{arc }TR), and (\text{arc }PT = 80^{\circ}), so (\text{arc }TR=180 - 80=100^{\circ}).
Step3: Find the measure of arc (SR)
The measure of arc (SR) is (100^{\circ}) because vertical - angles formed by the intersection of two diameters in a circle result in equal - measure arcs.
Answer:
(100^{\circ})