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°.
