Question

1. Use complete sentences to explain how the special angles created by the Intersection of A and B by D can beused to solve for x.2. Solve for x, showing all of your work.3. Find the measure of <6.

Answer 1

According to the graph we have:

1. If the lines A and B cut by the secant D are parallel, then the collateral angles are supplementary, i.e. add up to 180°. In this case:

`(3x+7)+(4x+5)=180`

2. Solve for x:

`\begin{gathered} 3x+7+4x+5=180 \\ 7x+12=180 \\ 7x+12-12=180-12 \\ 7x=168 \\ (7x)/(7)=(168)/(7) \\ x=24 \end{gathered}`

Answer: x = 24

3. Angle 6 corresponds to angle 3x + 7 so they are equal. So:

`\angle6=3x+7`

Where: x = 24

Substitute the value:

`\angle6=3(24)+7=72+7=79`

Answer: <6 = 79°