### Video Transcript

In the figure below, given that
π΄π΅πΆπ· is a parallelogram, find the measure of angle π΄.

In this question, weβre given that
there is a parallelogram, and we need to find one of the angles in this
parallelogram. So, letβs recall what we know about
the angles. We can remember that in a
parallelogram, opposite angles are equal. Weβre asked to find the measure of
angle π΄. And if we know the angle at πΆ,
then these would be equal. If we look at the diagram, this
angle πΆπ·πΉ, we donβt know the value of. And if we wanted to work out the
angle π΄ directly, weβd need to know this angle at π΄π·πΈ. But we donβt.

There is another option to work out
the measure of angle π΄. And that is, if we know the angle
at π· or the angle at π΅. Letβs see if we can calculate this
angle at π΅. Letβs highlight this quadrilateral
within the shape π·πΈπ΅πΉ. We have a right angle here at angle
π·πΈπ΄. As it lies on the straight line
π΄π΅, then we can also say that there is a 90 degree or right angle here at
π·πΈπ΅. So, in this quadrilateral π·πΈπ΅πΉ,
we have three angles that we know and one that we donβt know. We can use the fact that the angles
in any quadrilateral sum to 360 degrees to find the measure of angle π΅.

So, angle π΅ is 130 degrees. Because opposite angles in a
parallelogram are equal, then π΅ and π· are both 130 degrees. So, letβs go back to looking at
π΄π΅πΆπ·. As the sum of the angles in this
parallelogram will be 360 degrees, if we take away two lots of 130 degrees from 360
degrees, then we know that π΄ and πΆ will add to 100 degrees.

Since we know that π΄ and πΆ are
equal, then both of these would be 50 degrees. So, the measure of angle π΄ is 50
degrees.