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

Given that π‘‹π‘ŒπΎπ‘€ β‰Œ 𝐴𝐡𝐢𝑀, find the measure of βˆ πΎπ‘€πΆ.

01:25

Video Transcript

Given that π‘‹π‘ŒπΎπ‘€ is congruent to 𝐴𝐡𝐢𝑀, find the measure of angle 𝐾𝑀𝐢.

In this question, we have two congruent quadrilaterals, 𝐴𝐡𝐢𝑀 on the left side of the diagram and π‘‹π‘ŒπΎπ‘€ on the right. We’re asked to find the measure of angle 𝐾𝑀𝐢, which is outside of these quadrilaterals. If we knew the measure of this angle, 𝐢𝑀𝐴, 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 π‘‹π‘ŒπΎπ‘€ would be congruent with angle 𝐴 in the quadrilateral 𝐴𝐡𝐢𝑀. So, therefore, the angle 𝑀 in quadrilateral 𝐴𝐡𝐢𝑀 is congruent to the angle 𝑀 in quadrilateral π‘‹π‘ŒπΎπ‘€.

So, therefore, the missing angle 𝐢𝑀𝐴 in quadrilateral 𝐴𝐡𝐢𝑀 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 𝐾𝑀𝐢 is equal to 180 degrees subtract 53 degrees subtract 53 degrees. And, therefore, the measure of angle 𝐾𝑀𝐢 is 74 degrees.

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