Question

A diagonal support beam is attached to the gate of a fence as shown. Which angles must be congruent in order for the top and bottom sides of the gate to be parallel?

A)
∠ 1 and ∠ 2


B)
∠ 3 and ∠ 4


C)
∠ 1 and ∠ 4


D)
∠ 1 and ∠ 3
A diagonal support beam is attached to the gate of a fence as shown. Which angles must be congruent in order for the top and bottom sides of the gate to be parallel?

A)
∠ 1 and ∠ 2


B)
∠ 3 and ∠ 4


C)
∠ 1 and ∠ 4


D)
∠ 1 and ∠ 3

Answer 1

From the given diagram, if the top and bottom sides of the gate are parallel, then
m∠1 = m∠4.

Also, if the vertical sides of the gate are perpendicular to the horizontal sides, then
m∠3 = m∠2

Answer: C) m∠1 and m∠4

Answer 2

Answer:C) ∠ 1 and ∠ 4

Explanation:

Given: A diagonal support beam is attached to the gate of a fence.

If the top and bottom sides of the gate to be parallel , then the alternate interior angles must be congruent.[ because if two lines are parallel the alternate interior made by transversal must be congruent]

Thus, C is the right option as ∠ 1 and ∠ 4 are the only alternate interior pair given in options .