Question

Two parallel lines are cut by a transversal. Angle 1 measures (4x + 28)°, and the angle adjacent to the alternate exterior angle with angle 1 measures (14x + 8)°. What is the value of x?

Answer 1

I am trying to picture this in my head....
I believe ur angles when added, are going to equal 180 degrees.
so let set them up to equal 180

4x + 28 + 14x + 8 = 180
18x + 36 = 180
18x = 180 - 36
18x = 144
x = 144/18
x = 8

Answer 2

The value of x = 8

Explanation:

For better understanding of the solution, see the attached figure of the diagram :

∠1 and ∠2 are alternate exterior angle and ∠3 is adjacent to ∠2

⇒ ∠1 = (4x + 28)°

⇒ ∠3 = (14x + 8)°

Now, ∠2 + ∠3 = 180° (Linear Pair)

⇒ ∠2 = 180 - 14x -8

⇒ ∠2 = 172 - 14x

Since the alternate exterior angles formed by the transversal between two parallel lines are equal in measure.

⇒ ∠1 = ∠2

⇒ (4x + 28)° = (172 - 14x)°

⇒ 18x = 144

⇒ x = 8

Therefore, ∠1 = ∠2 = 60° and ∠3 = 120°

Hence, The value of x = 8