### Video Transcript

From the figure, in which the
measure of angle πΆπ·π΄ is five π₯ degrees, the measure of angle π΅πΆπ· is seven π¦
degrees, and the measure of angle π΄π΅πΆ is eight π¦ degrees, find the values of π₯
and π¦.

Letβs begin by adding what weβve
been told to our figure. The measure of angle πΆπ·π΄ is five
π₯; thatβs this one. The angle π΅πΆπ· is seven π¦;
thatβs this one. And the measure of angle π΄π΅πΆ,
thatβs this one, is eight π¦. Okay, so how does this help us? Well, we have a couple of useful
facts. Firstly, we know that the sum of
the interior angles in a quadrilateral, thatβs a four-sided polygon, is 360
degrees. So according to our diagram, we can
say that eight π¦ plus seven π¦ plus five π₯ plus 85 equals 360. Letβs add seven π¦ and eight π¦ to
get 15π¦.

Then we spot that we have two
parallel lines in our diagram. The parallel lines are π΅π΄ and
πΆπ·. We can quote that cointerior angles
sum to 180 degrees. So these two angles, 85 and 5π₯,
are cointerior. They add to 180. And we form a second equation; this
time, 85 plus five π₯ equals 180. Letβs solve this equation for
π₯. We subtract 85 from both sides, so
five π₯ is equal to 95. Then we divide through by five. So π₯ is 95 divided by five, which
is 19. Remember, we still need to
calculate the value of π¦. So letβs clear some space.

Weβre going to go back to the first
equation we formed and substitute π₯ equals 19. When we do, we get 15π¦ plus five
times 19 plus 85 equals 360. Thatβs 15π¦ plus 95 plus 85 equals
360. 95 plus 85 is 180. So we have an equation in π¦ that
we can solve. We subtract 180 from both
sides. So 15π¦ is 180. And then, we divide through by
15. π¦ is 180 divided by 15, which is
equal to 12. So π₯ is 19 and π¦ is equal to
12.

Now, with angle questions, thereβs
often more than one way to answer them. We could have used the fact that
the angles at π΅ and πΆ are cointerior. They sum to 180 degrees. We form an equation, and we get
eight π¦ plus seven π¦ equals 180. So 15π¦ is equal to 180. Once again, we solve this equation
by dividing by 15. And we get π¦ is equal to 12.