# Question Video: Finding the Size of an Angle in a Circle Using Colloralies of Parallel Chords Mathematics

Given that the πβ ππ΄πΆ = 48Β°, find πΏ.

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### Video Transcript

Given that the measure of angle ππ΄πΆ equals 48 degrees, find πΏ.

Letβs identify what we know based on this image. The figure tells us that line segment π΄πΆ is parallel to line segment ππ΅. Since these two lines are parallel, this angle ππ΄πΆ and this angle π΄ππ΅ are supplementary angles. The two of them when added together equal 180 degrees.

We know that ππ΄πΆ is 48 degrees. If we solve this statement, we can find the measure of angle π΄ππ΅. Subtract 48 degrees from both sides, and we find out that the measure of angle π΄ππ΅ is 132 degrees. This is not enough information to solve. We also need to know this: the measure of an inscribed angle.

For us, the angle π΅πΆπ΄ is half the measure of the central angle subtended by the same arc. Which angle is that? That would be this angle. The measure of angle π΅πΆπ΄ is equal to one-half of the central angle. But how will we find out what the central angle is?

We know that a circle is 360 degrees, and we know that the measure of angle π΄ππ΅ is 132 degrees. 360 minus 132 equals 228 degrees. The central angle subtended by the arc π΅πΆπ΄ equals 228 degrees. One-half of 228 equals 114 degrees, and that means πΏ equals 114 degrees.