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

Video Transcript

Find the measure of angle 𝐶𝐴𝐸.

If we let angle 𝐶𝐴𝐸 equal 𝑥 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 𝐴𝐹𝐵 is equal to 95 degrees as opposite angles are equal. Next, we can see that angle 𝐹𝐵𝐴 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 𝐹𝐴𝐵 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 𝐶𝐴𝐸 and angle 𝐹𝐴𝐵 add up to 180.

As angle 𝐹𝐴𝐵 is equal 41 degrees, we can say that 𝑥 plus 41 equals 180. Subtracting 41 from both sides of this equation gives us a value of 𝑥 of 139 degrees. This means that angle 𝐶𝐴𝐸 is equal to 139 degrees.