Answer:
C. 124°
Step-by-step explanation:
The angles that have measurements given must add up to 180 because together they create a straight line, which is 180°.
To solve, set up an equation like this: [tex]\frac{2}{3}[/tex]x + x + 40 = 180. Combine the [tex]\frac{2}{3}[/tex]x and x to get 1 [tex]\frac{2}{3}[/tex]x. Then, subtract 40 from both sides and you'll end up with the equation 1 [tex]\frac{2}{3}[/tex]x = 140.
Divide by sides by 1 [tex]\frac{2}{3}[/tex] and the answer is x = 84.
Now you know the measure of x. Since angle ACD and angle BCE and vertical angles, they must have the same measure.
To solve, just find the measure of ACD by inputting 84 into the equation x+40. The answer is 124, meaning that the measure of angle BCE is also 124°.
I hope this makes sense and helps! Feel free to ask for clarification! ☺
