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

Given that β³π΄π΅πΆ β β³πππ, find πβ πΆ.

01:20

### Video Transcript

Given that triangle π΄π΅πΆ is congruent to triangle πππ, find the measure of angle πΆ.

So, here, we have two congruent triangles and weβre asked to work out the missing angle, πΆ. 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 π΄. And this will be congruent to angle π in triangle πππ. And as weβre told that this angle π is 40 degrees, this means that angle π΄ in triangle π΄π΅πΆ will also be 40 degrees.

We can also see that angle πΆ in triangle π΄π΅πΆ is congruent to angle π in triangle πππ. But weβre not given an angle measure for angle π. So, we canβt use this directly to help us work out angle πΆ. Instead, we can use the fact that the angles in a triangle add up to 180 degrees to find the measure of angle πΆ. Therefore, the measure of angle πΆ 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 πΆ is 84 degrees.