Question

Solving for Angles with Transversal Lines
Lines l and m are parallel.

Parallel lines l and m are intersected by lines s and t. At the intersection of lines l, s, and t, clockwise from the top left, the angles are blank, 50 degrees, (x + 25) degrees, (2 x) degrees, 1, blank. Lines t, s, and m create a triangle with angles 1, 2, 3.

Use the diagram to determine the measure of ∠3.

m∠3 =
°

Answer 1

m∠3 = 70°

Reason: At the intersection on l, the angle labeled 1 is vertically opposite the 50° angle, so ∠1 = 50°. Corresponding angles (from the parallel lines l || m) give ∠2 = x + 25 and ∠3 = 2x. In the triangle formed by s, t, and m,
50 + (x + 25) + 2x = 180.
So 3x + 75 = 180 → 3x = 105 → x = 35. Thus ∠3 = 2x = 70°.