Question Video: Finding the Size of an Angle in a Triangle given the Other Two Angles’ Sizes Using the Properties of Tangents Mathematics • Third Year of Preparatory School

Video Transcript

𝐵𝐶 is tangent to the circle 𝑀 at 𝐵. Find the measure of the angle 𝐴𝐵𝐶.

In order to calculate the angle 𝐴𝐵𝐶, we firstly need to consider the triangle 𝐴𝐵𝑀. The length 𝐴𝑀 is equal to the length 𝑀𝐵 as they are both radii of the circle. This means that triangle 𝐴𝐵𝑀 is isosceles. As the triangle is isosceles, angle 𝑀𝐴𝐵 is equal to angle 𝑀𝐵𝐴. Both of these angles are equal to 33 degrees.

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

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