Question Video: Properties of Parallel Lines Mathematics • First Year of Preparatory School

Video Transcript

From the information in the figure below, find the measure of angle 𝐴𝐸𝐶.

Angle 𝐴𝐸𝐶 is shown in the diagram. This can be split into the sum of two other angles, angle 𝐴𝐸𝐹 and angle 𝐶𝐸𝐹. We can use our angle properties involving parallel lines to calculate these two values. The lines 𝐴𝐵, 𝐸𝐹, and 𝐶𝐷 are parallel as indicated on the diagram. We know that alternate angles are congruent. These are sometimes referred to as “zee” or “zed” angles. This means that angle 𝐵𝐴𝐸 is equal to angle 𝐴𝐸𝐹. They’re both equal to 92 degrees.

Cointerior or supplementary angles sum to 180 degrees. These are often known as C angles. In this question, angle 𝐶𝐸𝐹 plus 131 degrees is equal to 180 degrees. This means that our missing angle 𝑦, angle 𝐶𝐸𝐹, is equal to 49 degrees. We can therefore calculate the measure of angle 𝐴𝐸𝐶 by adding 92 degrees and 49 degrees. This is equal to 141 degrees.