Answer: 54
Step-by-step explanation:
1) First, we need to find what 'x' is. We know that the exterior angles of a triangle equal to 360. So, we will add up all the expressions and set them equal to 360.
7x-2 + 9x-31 + 4x +33 = 360.
2) We will add all the like terms, which will give us: 20x + 0 = 360. We don't need to add the 0.
3) Now, we will isolate the 'x' by dividing 360 by 20 and we will get: x= 18.
4) To find the measure of angle DCE, we just have to substitute x in '7x-2' with 18, which then would equal to: 124.
5) Now, that we have the adjacent angle of DCE, we just have to subtract 124 from 180, and we will get the answer.
6) Angle DCE equals to 54.