Question Video: Finding the Measure of an Inscribed Angle given Its Arc’s Measure by Solving Two Linear Equations | Nagwa Question Video: Finding the Measure of an Inscribed Angle given Its Arc’s Measure by Solving Two Linear Equations | Nagwa

# Question Video: Finding the Measure of an Inscribed Angle given Its Arcβs Measure by Solving Two Linear Equations Mathematics • Third Year of Preparatory School

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From the figure, what is π₯?

01:53

### Video Transcript

From the figure, what is π₯?

Letβs start with what we know. We have angle π΄πΆπ΅, which measures 101 degrees. And we have angle π΄ππ΅. In this case, weβre talking about the reflex of angle π΄ππ΅. Thatβs the one thatβs greater than 180 degrees, which measures two π₯ plus eight degrees. Angle π΄πΆπ΅ and angle π΄ππ΅ share the endpoints π΄ and π΅. But because the vertex of angle π΄ππ΅ is the center of the circle, we say that angle π΄ππ΅ is a central angle for this circle. While the vertex for angle π΄πΆπ΅ is on the outside of the circle, making angle π΄πΆπ΅ an inscribed angle of the circle. And these three facts point us to the central angle theorem.

And the central angle theorem tells us that when a central angle and an inscribed angle share the same endpoints, the central angle will be two times that of the inscribed angle. In this diagram, the inscribed angle is π degrees, and that would make the central angle two π degrees. By this, we can say that the measure of angle π΄ππ΅ is going to be equal to two times the measure of angle π΄πΆπ΅. The measure of the central angle will be equal to two times the measure of the inscribed angle. And so, we can say that two π₯ plus eight will be equal to two times 101. When we multiply two times 101, we get 202. And now, weβre ready to solve for π₯. Subtract eight from both sides. Two π₯ equals 194. Then, divide both sides by two, and we find that π₯ equals 97.

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