Video Transcript
In the figure, 𝐶𝐷 and 𝐵𝐸 are
parallel. Find the measure of angle
𝐴𝐵𝐸.
We are told in the question that
the lines 𝐶𝐷 and 𝐵𝐸 are parallel. We’re asked to calculate the size
of angle 𝐴𝐵𝐸 denoted by the letter 𝑥. We can see from the diagram that
𝐴𝐵𝐶𝐷 is a quadrilateral, a four-sided shape. The angles in any quadrilateral sum
to 360 degrees. This means that the sum of the
missing angle 𝑦, 90 degrees, 131 degrees, 69 degrees must equal 360 degrees. Simplifying the left-hand side
gives us 𝑦 plus 290 is equal to 360. Subtracting 290 from both sides
gives us 𝑦 is equal to 70. The missing angle in the
quadrilateral is 70 degrees.
We can now use the fact that
cointerior or supplementary angles sum to 180 degrees. These are also sometimes known as C
angles. In this question, 70 plus 69 plus
𝑥 must equal 180. This can be simplified to 𝑥 plus
139 is equal to 180. Subtracting 139 from both sides of
this equation gives us 𝑥 is equal to 41. We can therefore conclude that the
measure of angle 𝐴𝐵𝐸 is 41 degrees.
