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.
