Question

pre-algebra ic sem 2 fall 2025
semester a

which correctly describes how to determine the measure of ∠1?
the 81° angle and ∠2
are corresponding
angles so ∠2 must
measure 81°. angles 1
and 2 are
supplementary angles
so ∠1 must measure
99°.
the 81° angle and ∠2
are alternate interior
angles so ∠2 must
measure 99°. angles 1
and 2 are
supplementary angles
so ∠1 must measure
81°.
the 81° angle and ∠2
are alternate interior
angles so ∠2 must
measure 81°. angles 1
and 2 are
supplementary angles
so ∠1 must measure
99°.
the 81° angle and ∠2
are corresponding
angles so ∠2 must
measure 99°. angles 1
and 2 are
supplementary angles
so ∠1 must measure
81°.

Explanation:

Step1: Identify relationship between \(81^{\circ}\) angle and \(\angle2\)

The \(81^{\circ}\) angle and \(\angle2\) are corresponding angles. By the Corresponding Angles Theorem, if two parallel lines are cut by a transversal, corresponding angles are congruent. So \(\angle2 = 81^{\circ}\) is incorrect. Wait, no, actually, let's re - check. Wait, no, the first option says: The \(81^{\circ}\) angle and \(\angle2\) are corresponding angles so \(\angle2\) must measure \(81^{\circ}\). Angles \(1\) and \(2\) are supplementary angles (\(\angle1+\angle2 = 180^{\circ}\)). If \(\angle2=81^{\circ}\), then \(\angle1=180^{\circ}-\angle2=180 - 81=99^{\circ}\)

Step2: Analyze other options

• For the second option: Alternate interior angles would be equal. If the \(81^{\circ}\) angle and \(\angle2\) were alternate interior angles, \(\angle2 = 81^{\circ}\), not \(99^{\circ}\). And if \(\angle1+\angle2=180^{\circ}\), \(\angle1

eq81^{\circ}\)

• For the third option: Alternate interior angles are equal. If \(\angle2 = 81^{\circ}\), then \(\angle1=180 - 81=99^{\circ}\) (correct relationship as supplementary angles, but the first part about alternate interior is wrong)
• For the fourth option: Corresponding angles are equal (\(\angle2 = 81^{\circ}\)), then \(\angle1=180 - 81=99^{\circ}

eq81^{\circ}\)

Answer:

The first option: The \(81^{\circ}\) angle and \(\angle2\) are corresponding angles so \(\angle2\) must measure \(81^{\circ}\). Angles \(1\) and \(2\) are supplementary angles so \(\angle1\) must measure \(99^{\circ}\)