Find the measure of angle 𝐶.
We can see from the diagram that
the line 𝐴𝐵 is parallel to the line 𝐶𝐷. In this question, we need to
calculate the measure of angle 𝐶. We begin by looking at the point
𝐴, noting that angles at a point or in a circle sum to 360 degrees. If we let the missing angle be 𝑥,
then 𝑥 plus 123 plus 132 is equal to 360. Simplifying this gives us 𝑥 plus
255 is equal to 360. Subtracting 255 from both sides of
this equation gives us 𝑥 is equal to 105. The missing angle at point 𝐴 is
As mentioned previously, lines 𝐴𝐵
and 𝐶𝐷 are parallel. The line 𝐴𝐶 creates two
cointerior or supplementary angles. As these sum to 180 degrees, the
angle 𝑦 at point 𝐶 plus 105 must equal 180. Subtracting 105 from both sides of
this equation gives us 𝑦 is equal to 75. We can therefore conclude that the
measure of angle 𝐶 is equal to 75 degrees.