# Question Video: Finding the Measure of an Angle in the Triangle of a Circumcircle Mathematics

Find πβ π΅.

01:51

### Video Transcript

Find the measure of angle π΅.

In this question, weβre asked to find the measure of one of the angles in the triangle π΄π΅πΆ. In order to do this, we will recall some of the properties of circles. Letβs begin by considering the chords π΄π΅ and π΄πΆ. These two chords are equidistant from the center of the circle π such that line segment ππ is equal to line segment ππ. We recall that if two chords are equidistant from the center of a circle, their lengths are equal. This means that chord π΄π΅ is equal in length to chord π΄πΆ, and triangle π΄π΅πΆ is therefore isosceles. In any isosceles triangle, two angles are equal, in this case the angles at π΅ and πΆ.

If we let the measure of angle π΅ be π₯, then we can calculate this using our knowledge of angles in triangles. We know that angles in a triangle sum to 180 degrees. This means that π₯ plus π₯ plus 35 degrees is equal to 180 degrees. π₯ plus π₯ is equal to two π₯. And subtracting 35 degrees from both sides, we have two π₯ is equal to 145 degrees. We can then divide through by two such that π₯ is equal to 72.5 degrees. The measure of angle π΅ is 72.5 degrees.