Question

Lines x and y are parallel.

Use the diagram to determine the measure of the unknown angle.

m∠1 = (6x + 8)°
m∠1 = 74°

1. What is the value of x? _____ Options: 11, 16, 22, 31.

2. What is the measure of ∠2?
(7x - 2)° + m∠2 = 106°

m∠2 = ____° Options: 21, 27, 31, 37.

Answer 1

all work is shown and pictured

Answer 2

On the bottom line, the 106 and number 1 make a straight line and needs to equal 180 degrees.

This means number 1 = 180-106 = 74 degrees.

Because x and y are parallel, the top outside angle is the same as number 1.

6x +8 = 74

Subtract 8 from both sides:

6x = 66

divide both sides by 6:

x = 66 / 6

x = 11

Now you have x, replace x in the equation for 7x-2 to find that angle:

7(11) -2 = 77-2 = 75 degrees.

The three inside angles need to equal 180 degrees.

Angle 2 = 180 - 74 - 75 = 31 degrees.