# Question Video: Finding the Measure of a Central Angle Given the Measure of Its Arc Mathematics • 11th Grade

Find the value of π₯ given that π of the arc π΄π· = 34Β°.

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### Video Transcript

Find the value of π₯ given that the measure of the arc π΄π· equals 34 degrees.

Letβs look carefully at the diagram weβve been given. There is a circle with its center at the point π. Points π΄ and π΅ lie on the circumference of the circle. And the line segment connecting them passes through the center, so it is a diameter. There are two further points on the circleβs circumference, point πΆ and point π·. And the radii connecting each of these points to the center of the circle, the line segments πΆπ and π·π, have also been drawn.

Weβre given in the question that the measure of the arc π΄π· is 34 degrees. We should recall that this notation means the minor arc connecting points π΄ and π·. Itβs this arc here now highlighted in pink. We are asked to determine the value of π₯, which we can see is the measure of the angle formed between the two radii π·π and π΄π.

Another way of describing this angle is as the central angle of the arc π΄π·. Itβs the angle formed between the two radii connecting the endpoints of the arc π΄π· to the center of the circle. We can therefore recall a definition which relates the measure of an arc to the measure of its central angle. The measure of an arc is equal to the measure of its central angle. So, we have that the measure of the arc π΄π· is equal to π₯ degrees.

The measure of the arc π΄π· is 34 degrees, so we have 34 degrees equals π₯ degrees. And as both sides of this equation are measured in degrees, we find that π₯ is equal to 34. So by recalling that the measure of an arc is the measure of its central angle, we found the value of π₯ is 34.