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.
