# Question Video: Finding the Measure of an Angle Given Its Supplementary Angleβs Measure Mathematics • 8th Grade

In the figure, πΈπ intersects π΄π΅ and πΆπ· at π and πΉ respectively. Find πβ πΈπΉπΆ.

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### Video Transcript

In the figure, πΈπ intersects π΄π΅ and πΆπ· at π and πΉ, respectively. Find the measure of angle πΈπΉπΆ.

The lines through π΄π΅ and πΆπ· are parallel as indicated on the diagram. The line πΈπ is a transversal line that cuts the two parallel lines. We have been asked to work out the value of angle πΈπΉπΆ. In order to answer this question, we will use our angle properties relating to parallel lines.

We know that vertically opposite angles are equal. This means that angle πΈππ΅ is equal to angle π΄ππΉ. Both of these are equal to 84 degrees. We also know that cointerior or supplementary angles sum to 180 degrees. These are often referred to as C angles, as shown in the diagram. Angles π΄ππΉ and πΈπΉπΆ must sum to 180 degrees. This means that 84 plus angle πΈπΉπΆ is equal to 180. Subtracting 84 from both sides of this equation gives us angle πΈπΉπΆ is equal to 96. The measure of angle πΈπΉπΆ is equal to 96 degrees.