Video: Finding the Measure of an Angle Bounded between Two Congruent Quadrilaterals

Video Transcript

Given that 𝑋𝑌𝐾𝑀 is congruent to 𝐴𝐵𝐶𝑀, find the measure of angle 𝐾𝑀𝐶.

In this question, we have two congruent quadrilaterals, 𝐴𝐵𝐶𝑀 on the left side of the diagram and 𝑋𝑌𝐾𝑀 on the right. We’re asked to find the measure of angle 𝐾𝑀𝐶, which is outside of these quadrilaterals. If we knew the measure of this angle, 𝐶𝑀𝐴, we could calculate the missing angle. We can use the congruency statement to help us work out this angle. We could see, for example, that angle 𝑋 in the quadrilateral 𝑋𝑌𝐾𝑀 would be congruent with angle 𝐴 in the quadrilateral 𝐴𝐵𝐶𝑀. So, therefore, the angle 𝑀 in quadrilateral 𝐴𝐵𝐶𝑀 is congruent to the angle 𝑀 in quadrilateral 𝑋𝑌𝐾𝑀.

So, therefore, the missing angle 𝐶𝑀𝐴 in quadrilateral 𝐴𝐵𝐶𝑀 would be 53 degrees. We can use the fact that the angles on a straight line add up to 180 degrees to work out that our angle 𝐾𝑀𝐶 is equal to 180 degrees subtract 53 degrees subtract 53 degrees. And, therefore, the measure of angle 𝐾𝑀𝐶 is 74 degrees.