### Video Transcript

In the figure below, π·π΅πΆ is an
isosceles triangle, angle πΆπ΅π· has measure 40 degrees, angle π·πΆπΈ has measure 15
degrees, angle π΅π·πΆ has measure eight π₯ plus 20, and angle πΈπ΅πΆ has measure 11
times π¦ minus two. Find the values of π₯ and π¦.

Letβs find π₯ first. Since π·π΅πΆ is an isosceles
triangle, we know that angles π·πΆπ΅ and πΆπ΅π· are equal. Therefore, angle π΅π·πΆ has measure
180 minus 40 minus 40, which is 100 degrees. The question tells us that the
measure of angle π΅π·πΆ is equal to eight π₯ plus 20 degrees. Substituting in our value of 100
for the measure of π΅π·πΆ and simplifying, we find that π₯ equals 10.

Since angles π·π΅πΈ and π·πΆπΈ are
subtended by the same arc, they must be equal. We are told that the measure of
π·πΆπΈ is 15 degrees. Therefore, the measure of π·π΅πΈ is
15 degrees too. Therefore, angle πΈπ΅πΆ, which is
the sum of angles πΆπ΅π· and π·π΅πΈ, has measure 40 plus 15, which is 55. We are told that the measure of
πΈπ΅πΆ is equal to 11 times π¦ minus two degrees. We can now substitute in our value
of 55 for the measure of πΈπ΅πΆ and simplify, giving us π¦ equals seven. The answer to the question is π₯
equals 10 and π¦ equals seven.