Question Video: Using the Properties of Parallel Lines to Solve a Problem | Nagwa Question Video: Using the Properties of Parallel Lines to Solve a Problem | Nagwa

# Question Video: Using the Properties of Parallel Lines to Solve a Problem Mathematics • First Year of Preparatory School

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In the figure, given that πβ π΄πΆπΈ = 131Β°, find πβ πΆπΈπΉ.

02:21

### Video Transcript

In the figure below, given that the measure of angle π΄πΆπΈ equals 131 degrees, find the measure of angle πΆπΈπΉ.

Letβs start by marking on the angle measure of π΄πΆπΈ, which is 131 degrees, onto the diagram. The measure of angle πΆπΈπΉ 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·πΆ, and πΈπΉ, 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΄πΆ, then the two angles colored green β thatβs angle πΆπ΄π΅ and angle π΄πΆπ· 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΄πΆπ· and πΆπ΄π΅ are equal in measure. And as the measure of angle πΆπ΄π΅ is 95 degrees, then the measure of angle π΄πΆπ· is also 95 degrees.

We can then work out the measure of the remaining part of this angle π΄πΆπΈ, the angle π·πΆπΈ. Its measure will be found by subtracting 95 degrees from 131 degrees, which is 36 degrees. So, to find the measure of angle πΆπΈπΉ, we can use the same property of parallel lines again. This time, we can consider the parallel line segments π·πΆ and πΈπΉ and the transversal of line segment πΆπΈ. Then, we can recognize that the angles π·πΆπΈ and πΆπΈπΉ 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 πΆπΈπΉ is 36 degrees.

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