Applying the inscribed angle theorem, we have the following measures:
a. Measure of angle RQT = 79°
b. Measure of angle QTS = 51°
<h3>What is the Inscribed Angle Theorem?</h3>
Based on the inscribed angle theorem, the measure of an inscribed angle (i.e. angle RQT and angle QTS) of a circle is half the measure of each of their respective intercepted arcs (arc RQT and arc QRS).
Given the following:
Measure of arc RQT = 202°
Measure of angle QRS = 129°
a. Find the measure of angle RQT:
Measure of angle RQT = 1/2(360 - 202) [inscribed angle theorem]
Measure of angle RQT = 1/2(158)
Measure of angle RQT = 79°
b. Find the measure of angle QTS:
Measure of angle QTS = 1/2(360 - 2(measure of angle QRS)) [inscribed angle theorem]
Measure of angle QTS = 1/2(360 - 2(129))
Measure of angle QTS = 1/2(102)
Measure of angle QTS = 51°
In summary, applying the inscribed angle theorem, we have the following measures:
a. Measure of angle RQT = 79°
b. Measure of angle QTS = 51°
Learn more about the inscribed angle theorem on:
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