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?

The value of x = 8

Step-by-step 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

relating to or denoting a system of numbers and arithmetic based on the number ten, tenth parts, and powers of ten.

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