Video: Finding the Size of an Angle in a Triangle given the Other Two Angles’ Sizes Using the Properties of Tangents

𝐡𝐢 is tangent to the circle 𝑀 at 𝐡. Find π‘šβˆ π΄π΅πΆ.

01:21

Video Transcript

𝐡𝐢 is tangent to the circle 𝑀 at 𝐡. Find the measure of the angle 𝐴𝐡𝐢.

In order to calculate the angle 𝐴𝐡𝐢, we firstly need to consider the triangle 𝐴𝐡𝑀. The length 𝐴𝑀 is equal to the length 𝑀𝐡 as they are both radii of the circle. This means that triangle 𝐴𝐡𝑀 is isosceles. As the triangle is isosceles, angle 𝑀𝐴𝐡 is equal to angle 𝑀𝐡𝐴. Both of these angles are equal to 33 degrees.

As 𝐡𝐢 is a tangent, then we can see that 𝐡𝐢 meets 𝐡𝑀 at 90 degrees. A tangent will always meet the radius at 90 degrees. This means that πœƒ plus 33 must be equal to 90. Subtracting 33 from both sides of this equation gives us πœƒ equals 57.

This means that the measure of angle 𝐴𝐡𝐢 is equal to 57 degrees.

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