Video: Finding the Measure of an Angle Given Its Supplementary Angle’s Measure

Video Transcript

In the figure, 𝐸𝑁 intersects 𝐴𝐵 and 𝐶𝐷 at 𝑀 and 𝐹, respectively. Find the measure of angle 𝐸𝐹𝐶.

The lines through 𝐴𝐵 and 𝐶𝐷 are parallel as indicated on the diagram. The line 𝐸𝑁 is a transversal line that cuts the two parallel lines. We have been asked to work out the value of angle 𝐸𝐹𝐶. In order to answer this question, we will use our angle properties relating to parallel lines.

We know that vertically opposite angles are equal. This means that angle 𝐸𝑀𝐵 is equal to angle 𝐴𝑀𝐹. Both of these are equal to 84 degrees. We also know that cointerior or supplementary angles sum to 180 degrees. These are often referred to as C angles, as shown in the diagram. Angles 𝐴𝑀𝐹 and 𝐸𝐹𝐶 must sum to 180 degrees. This means that 84 plus angle 𝐸𝐹𝐶 is equal to 180. Subtracting 84 from both sides of this equation gives us angle 𝐸𝐹𝐶 is equal to 96. The measure of angle 𝐸𝐹𝐶 is equal to 96 degrees.