Calculate the measurement of angle 𝐶𝑀𝐹.
We’re asked to calculate the measurement of this angle, angle 𝐶𝑀𝐹. And we’re only given the measurement of one of the angles. This angle here measures 126 degrees. We’re going to need to calculate the measurements of some of the missing angles to help us find the measurement of angle 𝐶𝑀𝐹. Because opposite angles are equal, we can say that the second angle, marked in pink, also measures 126 degrees.
There are three smaller angles which are equal in size within this larger angle. Because these angles are equal in size and there are three of them, we know that they measure a third of 126 degrees. 126 divided by three is 42. So we know that each of these smaller angles measures 42 degrees. There are two of these angles within angle 𝐶𝑀𝐹. 42 doubled or multiplied by two is 84.
Now what we need to do is find this missing angle. We could use another known fact to help us. We know that angles on a straight line total 180 degrees. So we could add together the three lots of 42 degrees. This gives us a total of 126 degrees, which we can subtract from 180. 180 take away 126 is 54.
Now we have the measurements of each of the three angles which make up angle 𝐶𝑀𝐹, Two lots of 42 plus 54. 42 times two is 84. So we just need to add together 84 and 54. Four plus four is eight. Eight plus five is 13. The measurement of angle 𝐶𝑀𝐹 is 138 degrees.