Question

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

Answer 1

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.