# Question Video: Finding the Measure of an Angle of Tangency given the Measures of an Inscribed Angle and Arc Mathematics

Given that π΄π· is a tangent to the circle, find πβ π΅π΄π·.

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### Video Transcript

Given that π΄π· is a tangent to the circle, find the measure of angle π΅π΄π·.

The inscribed angle πΆπ΄π΅ is half the measure of the arc. This means that angle πΆπ΄π΅ is equal to 94 divided by two. 94 divided by two is equal to 47 degrees. The sum of the angles in a triangle equals 180 degrees. Therefore, angle π΄πΆπ΅ is equal to 180 minus 68 plus 47. This is equal to 65. Therefore, angle π΄πΆπ΅ is equal to 65 degrees.

The alternate segment theorem states that the angle at the tangent is equal to the opposite interior angle. In this case, angle π΅π΄π· or π³ is equal to angle π΄πΆπ΅. As angle π΄πΆπ΅ is equal to 65 degrees, then angle π΅π΄π· must also be equal to 65 degrees.

As π΄π· is a tangent to the circle, the angle π΅π΄π· is 65 degrees.