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
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.