Question

In the diagram, transversal t cuts parallel lines a and b. Which equation is necessarily true?

OA. m/1=m/7
OB.
O C.
O D.
m23=m26
m25+ m28 = 90°
m26+ m27 = 180°

Answer 1

A. ∠1 = ∠7

B. ∠2 = ∠6

D. ∠6 + ∠7 = 180°

Explanation:

⭐ Why A is correct

• ∠1 = ∠7 because when two parallel lines are cut by a transversal, alternate exterior angles are formed.
• Alternate exterior angles are congruent.
• ∠1 and ∠7 are alternate exterior angles.
• Therefore, ∠1 = ∠7.

⭐ Why B is correct

• ∠2 = ∠6 because when two parallel lines are cut by a transversal, corresponding angles are formed.
• Corresponding angles are congruent.
• ∠2 and ∠6 are corresponding angles.
• Therefore, ∠2 = ∠6.

❌ Why C is incorrect

• ∠5 + ∠8 is not equal to 90° because ∠5 and ∠8 are adjacent angles.
• Adjacent angles sum to 180°.
• Therefore, ∠5 + ∠8 is not equal to 90°.

⭐ Why D is correct

• ∠6 + ∠7 = 180° because ∠6 and ∠7 are adjacent angles.
• Adjacent angles sum to 180°.
• Therefore, ∠6 + ∠7 = 180°.