∠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.
[tex]\rm \angle 1=\angle 2\\\\4x+28=172-14x\\\\4x+14x=172-28\\\\18x=144\\\\x =\dfrac{144}{18}\\\\x=8[/tex]
Hence, the value of x is 8.
To know more about adjacent angles click the link given below.
https://brainly.com/question/1554343
