Question

Given the information about angles ZCDE and ZEDF, which of the following steps correctly justifies that they form a linear pair and are supplementary?

A) mZCDE + mZEDF = 180
B) 2x + (6x + 40) = 180
C) 7x + 40 = 180
D) 7x = 140
E) x = 20

Answer 1

The correct steps to justify that angles ZCDE and ZEDF form a linear pair and are supplementary include setting up an equation with their expressions, combining like terms, and solving for x to show their measures add to 180 degrees.

Step-by-step explanation:

To determine if angles ZCDE and ZEDF form a linear pair and are supplementary, we need to find out if their measures add up to 180 degrees. Given the expressions for the angles, we can set up an equation representing the sum of the angles:

m∠CDE is represented by 2x

m∠EDF is represented by 6x + 40

The step that justifies that angles ZCDE and ZEDF are supplementary is:

Combine like terms: (2x) + (6x + 40) = 8x + 40

Set up the equation to equal 180 degrees: 8x + 40 = 180

Subtract 40 from both sides: 8x = 140

Divide by 8: x = 20

Each step justifies that when x is 20, the sum of the angles will be 180 degrees, confirming they are supplementary.