Question Video: Using the Properties of Parallel Lines to Solve a Problem Mathematics • 8th Grade

In the figure, given that π‘šβˆ π΄πΆπΈ = 131Β°, find π‘šβˆ πΆπΈπΉ.


Video Transcript

In the figure below, given that the measure of angle 𝐴𝐢𝐸 equals 131 degrees, find the measure of angle 𝐢𝐸𝐹.

Let’s start by marking on the angle measure of 𝐴𝐢𝐸, which is 131 degrees, onto the diagram. The measure of angle 𝐢𝐸𝐹 that we need to calculate is at the bottom of the diagram. Now, we are given that there are three line segments, 𝐴𝐡, 𝐷𝐢, and 𝐸𝐹, 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 𝐴𝐢, then the two angles colored green β€” that’s angle 𝐢𝐴𝐡 and angle 𝐴𝐢𝐷 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 𝐴𝐢𝐷 and 𝐢𝐴𝐡 are equal in measure. And as the measure of angle 𝐢𝐴𝐡 is 95 degrees, then the measure of angle 𝐴𝐢𝐷 is also 95 degrees.

We can then work out the measure of the remaining part of this angle 𝐴𝐢𝐸, the angle 𝐷𝐢𝐸. Its measure will be found by subtracting 95 degrees from 131 degrees, which is 36 degrees. So, to find the measure of angle 𝐢𝐸𝐹, we can use the same property of parallel lines again. This time, we can consider the parallel line segments 𝐷𝐢 and 𝐸𝐹 and the transversal of line segment 𝐢𝐸. Then, we can recognize that the angles 𝐷𝐢𝐸 and 𝐢𝐸𝐹 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 𝐢𝐸𝐹 is 36 degrees.

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