If the line passing through 𝐴 and
𝐶 is a straight line, find the measure of angle 𝐴𝐵𝐶.
In this question, we are asked to
find the measure of an angle that lies on a given straight line. The easiest way to answer this
question is to recall that the measure of a straight angle, that is, an angle whose
sides form a straight line, is 180 degrees. This is enough to answer the
question. However, it can be useful to
understand why this angle is said to have measure 180 degrees.
To do this, we recall that an angle
is a rotation between two rays that share a starting point. And we define the measure of a full
turn to be 360 degrees. If we were to only perform half a
turn, then the sides would form a straight line. We would need to half the angle
measure to get 180 degrees. Hence, the measure of angle 𝐴𝐵𝐶
is 180 degrees.