Video: Finding the Size of an Angle Using the Parallel Lines Relation given Its Supplementary Angle’s Size

Find π‘šβˆ πΆπ΄πΈ.

01:41

Video Transcript

Find the measure of angle 𝐢𝐴𝐸.

If we let angle 𝐢𝐴𝐸 equal π‘₯ and the crossover point in the middle of the diagram be point 𝐹, we can solve this problem using our angle properties.

Firstly, we can see that angle 𝐴𝐹𝐡 is equal to 95 degrees as opposite angles are equal. Next, we can see that angle 𝐹𝐡𝐴 is equal to 44 degrees as alternate angles or 𝑍 angles are also equal.

Angles in a triangle have a sum of 180 degrees. This means that angle 𝐹𝐴𝐡 would be 41 degrees. 95 plus 44 is 139, and 180 minus 139 is 41. Angles on a straight line also add up to 180 degrees. This means that angles 𝐢𝐴𝐸 and angle 𝐹𝐴𝐡 add up to 180.

As angle 𝐹𝐴𝐡 is equal 41 degrees, we can say that π‘₯ plus 41 equals 180. Subtracting 41 from both sides of this equation gives us a value of π‘₯ of 139 degrees. This means that angle 𝐢𝐴𝐸 is equal to 139 degrees.

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