Question Video: Finding the Exterior Angle of a Triangle Given the Opposite Interior Angles Mathematics

Video Transcript

In the given figure, find the measure of the exterior angle, angle 𝐶.

If we look at the diagram, we can observe that we are given the measures of two of the interior angles of this triangle 𝐴𝐵𝐶. The measure of angle 𝐴 is 50 degrees, and the measure of angle 𝐵 is 55 degrees. We need to calculate the measure of this exterior angle at 𝐶, which is given as 𝑥.

The most efficient way to answer this question is to recall the property that the measure of any exterior angle of a triangle is equal to the sum of the measures of the opposite interior angles. This means that since 𝐴 and 𝐵 are the opposite interior angles to the exterior angle at 𝐶, we can say that 𝑥 is equal to 50 degrees plus 55 degrees. This gives us an answer of 105 degrees.

Alternatively, we could’ve used the fact that the three interior angles in the triangle add up to 180 degrees. We could therefore write that the measure of this interior angle 𝐵𝐶𝐴 is equal to 180 degrees subtract 50 degrees plus 55 degrees. This gives 75 degrees. We would then need to perform another calculation using the fact that the sum of these two angles at the vertex 𝐶 must be 180 degrees, because they lie on a straight line. So 𝑥 would be equal to 180 degrees subtract 75 degrees, and that would give us an answer of 105 degrees. Either method gives us the answer of 105 degrees.