Video: Finding the Measure of an Angle Using the Congruence Properties between Two Congruent Polygons

Video Transcript

Given that triangle 𝐴𝐵𝐶 is congruent to triangle 𝑋𝑌𝑍, find the measure of angle 𝐶.

So, here, we have two congruent triangles and we’re asked to work out the missing angle, 𝐶. Here, we can use the congruency statement to help us work out which corresponding angles would be congruent. The first angle we can look at is angle 𝐴. And this will be congruent to angle 𝑋 in triangle 𝑋𝑌𝑍. And as we’re told that this angle 𝑋 is 40 degrees, this means that angle 𝐴 in triangle 𝐴𝐵𝐶 will also be 40 degrees.

We can also see that angle 𝐶 in triangle 𝐴𝐵𝐶 is congruent to angle 𝑍 in triangle 𝑋𝑌𝑍. But we’re not given an angle measure for angle 𝑍. So, we can’t use this directly to help us work out angle 𝐶. Instead, we can use the fact that the angles in a triangle add up to 180 degrees to find the measure of angle 𝐶. Therefore, the measure of angle 𝐶 is equal to 180 degrees subtract 56 degrees and subtract 40 degrees, giving us 84 degrees. And so, our final answer is that the measure of angle 𝐶 is 84 degrees.