Video Transcript
In the figure below, given that the
measure of angle π΄πΆπΈ equals 131 degrees, find the measure of angle πΆπΈπΉ.
Letβs start by marking on the angle
measure of π΄πΆπΈ, which is 131 degrees, onto the diagram. The measure of angle πΆπΈπΉ that we
need to calculate is at the bottom of the diagram. Now, we are given that there are
three line segments, π΄π΅, π·πΆ, and πΈπΉ, which are all marked as parallel. And that will allow us to work out
some other angle measures.
If we take the top two parallel
lines and the transversal of line segment π΄πΆ, then the two angles colored green β
thatβs angle πΆπ΄π΅ and angle π΄πΆπ· β are alternate interior angles. And we can recall that if a
transversal cuts a pair of parallel lines, then the alternate interior angles are
equal in measure. So, angles π΄πΆπ· and πΆπ΄π΅ are
equal in measure. And as the measure of angle πΆπ΄π΅
is 95 degrees, then the measure of angle π΄πΆπ· is also 95 degrees.
We can then work out the measure of
the remaining part of this angle π΄πΆπΈ, the angle π·πΆπΈ. Its measure will be found by
subtracting 95 degrees from 131 degrees, which is 36 degrees. So, to find the measure of angle
πΆπΈπΉ, we can use the same property of parallel lines again. This time, we can consider the
parallel line segments π·πΆ and πΈπΉ and the transversal of line segment πΆπΈ. Then, we can recognize that the
angles π·πΆπΈ and πΆπΈπΉ are alternate interior angles. And once again, we know that these
angles must be equal in measure. So they are both 36 degrees.
Therefore, by using the properties
of parallel lines and transversals, we have determined that the measure of angle
πΆπΈπΉ is 36 degrees.
