Question

Lines I and m are parallel.

Answer 1

m∠3 = 70°

Solution:

Line l and line m are parallel.

line t and line s are transversals.

Sum of the adjacent angles in a straight line = 180°

50° + (x + 25)° + (2x)° = 180°

50° + x° + 25° + 2x° = 180°

75° + 3x° = 180°

Subtract 75° from both sides, we get

3x° = 105°

Divide by 3 on both sides of the equation.

x° = 35°

x = 35

(2x)° = (2 × 35)° = 70°

(2x)° and ∠3 are alternate interior angles.

If two lines are parallel then alternate interior angles are congruent.

m∠3 = (2x)°

m∠3 = 70°

Hence m∠3 = 70°.