Question Video: Finding the Measure of an Angle of Tangency given the Measures of an Inscribed Angle and Arc Mathematics • Third Year of Preparatory School

Video Transcript

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

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

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