m∠5 = x + 1
m∠5 = 60°
Solution:
Given data:
Line a and Line b are parallel lines.
The line that crosses both a and b is a transversal line.
m∠1 = x + 1 and m∠6 = 2x + 2.
If two parallel lines cut by a transversal, then their corresponding angles on the same side are congruent.
∠5 and ∠1 are corresponding angles.
⇒ m∠5 = m∠1
⇒ m∠5 = x + 1
Now, ∠5 and ∠6 forms a linear pair.
m∠5 + m∠6 = 180°
x + 1 + 2x + 2 = 180°
3x + 3 = 180°
Subtract 3 from both sides.
3x = 177°
Divide by 3 on both sides.
x = 59°
m∠5 = 59° + 1° = 60°
m∠5 = 60°