### Video Transcript

In the figure, πΈπ intersects π΄π΅
and πΆπ· at π and πΉ, respectively. Find the measure of angle
πΈπΉπΆ.

The lines through π΄π΅ and πΆπ· are
parallel as indicated on the diagram. The line πΈπ is a transversal line
that cuts the two parallel lines. We have been asked to work out the
value of angle πΈπΉπΆ. 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 πΈππ΅ is
equal to angle π΄ππΉ. 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΄ππΉ and πΈπΉπΆ must sum
to 180 degrees. This means that 84 plus angle
πΈπΉπΆ is equal to 180. Subtracting 84 from both sides of
this equation gives us angle πΈπΉπΆ is equal to 96. The measure of angle πΈπΉπΆ is
equal to 96 degrees.