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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Answer:
90 cm²
Step-by-step explanation:
Given that both triangles are similar, it follows that the ratio of their area equals the square of their corresponding sides.
Let the area of the other triangle be x. Therefore:
Cross multiply
Divide both sides by 16
90 = x
Area of the other polygon = 90 cm²