Question

Identify the theorem or postulate that is related to the measures of the angles in the pair, and find the unknown angle measures.
m∠1=(30x−30)∘, m∠5=(40x+70)∘


Alt. Int. ∠s Thm.

m∠1 = 30°, m∠5 = 150°

Alt. Int. ∠s Thm.

m∠1 = 30°, m∠5 = 30°

Same-Side Int. ∠s Thm.

m∠1 = 30°, m∠5 = 150°

Same-Side Int. ∠s Thm.

m∠1 = 150°, m∠5 = 30°

Answer 1

Angles formed when two parallel are intersected by a common transversal include, corresponding, alternate interior and exterior, same-side interior, and vertically opposite angles

The correct option is Same–Side Int. ∠s Thm. m∠1 = 30°, m∠5 = 150°

The reason the selection is correct is as follows:

The given angles are;

m∠1 = (30·x - 30)°. m∠5 = (40·x + 70)°

∠1, and ∠5, are located on the same side of the transversal and are both formed on the interior side of the parallel lines

Therefore, they are same–side interior angles

Same side interior angles theorem states that same side interior angles formed between parallel lines are supplementary

Therefore, we have;

m∠1 + m∠5 = 180°

Which gives;

(30·x - 30)° + (40·x + 70)° = 180°

(70·x + 40)° = 180°

70·x = 180° - 40° = 140°

$x = \dfrac{140^{\circ}}{70} = 2^{\circ}$

m∠1 = (30·x - 30)° = (30 × 2 - 30)° = 30°

m∠1 = 30°

m∠5 = (40·x + 70)° = (40 × 2 + 70)° = 150°

m∠5 = 150°

The correct option is therefore;

Same-Side Int. ∠s Thm. m∠1 = 30°, m∠5 = 150°

Learn more about parallel lines cut by a transversal here:

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