### Video Transcript

π΄π΅πΆ is parallel to πΉπΊπ». And πΉπ·π΅ is parallel to
πΊπΈπΆ. πΊπΈ is equal to πΈπ». Angle πΌπ»π½ is equal to 44
degrees. Work out the size of the angle
marked π₯. You must give reasons for your
answer.

Angle πΈπ»πΊ is equal to angle
πΌπ»π½, as opposite angles are equal. Therefore, angle πΈπ»πΊ is 44
degrees. We were told in the question that
πΊπΈ is equal to πΈπ». Therefore, triangle πΊπΈπ» is
isosceles.

As the triangle is isosceles, we
know that two angles will be equal. In this case, angle πΈπ»πΊ is equal
to angle π»πΊπΈ. They are both equal to 44
degrees. Finally, angles π»πΊπΈ and π΅πΆπΈ
are also equal. This is because they are alternate
angles or π angles.

As π΄π΅πΆ is parallel to πΉπΊπ», we
can draw letter π to show that these two angles are equal. Using the angle properties of
opposite angles, alternate angles, and the angles in an isosceles triangle, weβve
proved that π₯ is equal to 44 degrees.