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?
2 answers:
Answer:
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
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