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

Given that 𝐴𝐷 is a tangent to the circle, find π‘šβˆ π΅π΄π·.

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Video Transcript

Given that 𝐴𝐷 is a tangent to the circle, find the measure of angle 𝐡𝐴𝐷.

The inscribed angle 𝐢𝐴𝐡 is half the measure of the arc. This means that angle 𝐢𝐴𝐡 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 𝐴𝐢𝐡 is equal to 180 minus 68 plus 47. This is equal to 65. Therefore, angle 𝐴𝐢𝐡 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 𝐡𝐴𝐷 or 𝛳 is equal to angle 𝐴𝐢𝐡. As angle 𝐴𝐢𝐡 is equal to 65 degrees, then angle 𝐡𝐴𝐷 must also be equal to 65 degrees.

As 𝐴𝐷 is a tangent to the circle, the angle 𝐡𝐴𝐷 is 65 degrees.

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