Video: Finding the Measure of an Angle between One of Two Parallel Lines and the Side of a Given Quadrilateral

In the figure, 𝐢𝐷 and 𝐡𝐸 are parallel. Find π‘šβˆ π΄π΅πΈ.

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Video Transcript

In the figure, 𝐢𝐷 and 𝐡𝐸 are parallel. Find the measure of angle 𝐴𝐡𝐸.

We are told in the question that the lines 𝐢𝐷 and 𝐡𝐸 are parallel. We’re asked to calculate the size of angle 𝐴𝐡𝐸 denoted by the letter π‘₯. We can see from the diagram that 𝐴𝐡𝐢𝐷 is a quadrilateral, a four-sided shape. The angles in any quadrilateral sum to 360 degrees. This means that the sum of the missing angle 𝑦, 90 degrees, 131 degrees, 69 degrees must equal 360 degrees. Simplifying the left-hand side gives us 𝑦 plus 290 is equal to 360. Subtracting 290 from both sides gives us 𝑦 is equal to 70. The missing angle in the quadrilateral is 70 degrees.

We can now use the fact that cointerior or supplementary angles sum to 180 degrees. These are also sometimes known as C angles. In this question, 70 plus 69 plus π‘₯ must equal 180. This can be simplified to π‘₯ plus 139 is equal to 180. Subtracting 139 from both sides of this equation gives us π‘₯ is equal to 41. We can therefore conclude that the measure of angle 𝐴𝐡𝐸 is 41 degrees.

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