Question

What must be the value of x so line A and B are parallel lines cut by transversal f?

Answer 1

When x = 22 the lines a and b are parallel lines cut by transversal f.

Explanation:

Given : Measure of ∠CEF = 96° and measure of ∠HGB = (6x -36)°

We have to find the value of x so line a and b are parallel lines cut by transversal f.

Consider the given figure (we have renamed it as shown below)

Since, ∠CEF = 96°

Therefore, ∠AEG = 96° (vertically opposite angles)

Also for line a and b to be parallel the measure of angle ∠HGB and ∠AEG must be equal , then they form a pair of corresponding angles.

∠HGB = ∠AEG

(6x -36)° = 96°

adding 36 both side, we have ,

6x = 96 + 36

6x = 132

Divide both side by 6, we have,

x = 22

Thus, when x = 22 the lines a and b are parallel lines cut by transversal f.

Answer 2

Opposite exterior angles are congruent, so we can equate their measures and solve for x.

... 6x - 36 = 96

... x - 6 = 16 . . . . . . divide by 6

... x = 22 . . . . . . . . add 6

The value of x must be 22.