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lines AD and BE intersect at point C, as shown. create an expression that represents the measure of the angle DCE in terms if X

part 2 of question: using your expression, solve for the missing value of X if DCE was 120 degrees.

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Edufirst

Answer:

Please, find the image with the diagram of the lines corresponding to this question:

The answers are:

  • Equation: m ∠ DCE = 180º - x

  • Value of x = 60º

Explanation:

First question:

You must use the fact that the angles DCE and BCD are adjacent angles, because they share the vertex (C) and have a common side (CD).

Thus, as a first fact, the measure of the angle BCE is equal to the sum of the measures of the angles BCD and DCE.

On the other hand, BE is a straight line, thus the measure of angle BCE is 180º.

Hence, you can write:

  • m ∠ DCE + m ∠ DCB = 180º
  • m ∠ DCE + x = 180º
  • m ∠ DCE = 180º - x

Second question:

Solve for x:

  • Given: m ∠ DCE = 180º - x

  • Add x to both sides: m ∠ DCE + x  = 180º

  • Subtract m ∠ DCE from both sides: x = 180º - m ∠DCE

Substitute m ∠DCE with 120º:

  • x = 180º - 120º = 60º

Hence, for m ∠DCE = 120º, x = 60º.

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