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? One-half 2 8 12.

Answer 1

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

The value of x is 8.

Given

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)°.

Adjacent angles;

In geometry, two angles are adjacent if they have a common side and a common vertex.

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

∠1 = (4x + 28)°

∠3 = (14x + 8)°

Then,

∠2 + ∠3 = 180° ( Linear pair)

∠2 + 14x + 8 = 180

∠2 = 180 - 14x -8

∠2 = 172 - 14x

Therefore,

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

$\rm \angle 1=\angle 2\\\\4x+28=172-14x\\\\4x+14x=172-28\\\\18x=144\\\\x =\dfrac{144}{18}\\\\x=8$

Hence, the value of x is 8.

To know more about adjacent angles click the link given below.

brainly.com/question/1554343