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

Given that πππΎπ β π΄π΅πΆπ, find the measure of β πΎππΆ.

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### Video Transcript

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

In this question, we have two congruent quadrilaterals, π΄π΅πΆπ on the left side of the diagram and πππΎπ on the right. Weβre asked to find the measure of angle πΎππΆ, which is outside of these quadrilaterals. If we knew the measure of this angle, πΆππ΄, 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 π in the quadrilateral πππΎπ would be congruent with angle π΄ in the quadrilateral π΄π΅πΆπ. So, therefore, the angle π in quadrilateral π΄π΅πΆπ is congruent to the angle π in quadrilateral πππΎπ.

So, therefore, the missing angle πΆππ΄ in quadrilateral π΄π΅πΆπ 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 πΎππΆ is equal to 180 degrees subtract 53 degrees subtract 53 degrees. And, therefore, the measure of angle πΎππΆ is 74 degrees.