If m angle 1 = x , then p||q if (?)

Question

a .  m angle 3 = 180 - x 

b . m angle 4 = x

c . m angle 2 = 180 - x 

d . m angle 3 = x 

Answer 1

We’re told: If m∠1 = x, then p ∥ q if (?).

The multiple-choice options involve relationships between ∠1, ∠2, ∠3, and ∠4.

Step 1: Recall parallel line angle relationships

If two lines (p and q) are parallel and cut by a transversal, then:

1. Corresponding angles are equal.
2. Alternate interior angles are equal.
3. Consecutive (same-side) interior angles are supplementary (sum = 180°).

Step 2: Match with the answer choices

1. (a) m∠3 = 180 − x → this is a same-side interior angle rule.
2. (b) m∠4 = x → this could be corresponding or alternate interior.
3. (c) m∠2 = 180 − x → also supplementary case.
4. (d) m∠3 = x → this is alternate interior or corresponding.

Step 3: Identify the correct one

Usually in these standard diagrams:

1. ∠1 and ∠3 are alternate interior angles.
2. If m∠1 = x, then m∠3 must also equal x when p ∥ q.

So the correct answer is:

(d) m∠3 = x