Option B:
m∠7 = 65°
Solution:
Given data:
Line e and d are parallel and c is the transversal line.
m∠6 = (8x – 13)° and m∠3 = (4x + 1)°
∠6 and ∠3 are co-interior angles.
Co-interior angles add up to 180°.
m∠6 + m∠3 = 180°
⇒ (8x – 13)° + (4x + 1)° = 180°
⇒ 8x° – 13° + 4x° + 1° = 180°
⇒ 12x° – 12° = 180°
Add 12° on both sides of the equation.
12x° = 192°
Divide by 12° on both sides of the equation.
x° = 16°
Substitute x = 16 in ∠3.
m∠3 = (4x + 1)°
= (4 × 16 + 1)°
m∠3 = 65°
∠3 and ∠7 are corresponding angles.
Corresponding angles on the same side of the transversal are congruent.
m∠7 = m∠3
m∠7 = 65°
Option B is the correct answer.
