If m<1= x+ I and m<6= 2x + 2, what must m<5 be so the lines a and b are parallel?

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°

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