Question

lving 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.

Answer 1

Interpret the "1" as a label for an angle (not 1°). Label the six angles around the common intersection, clockwise from the top-left, A1, A2, A3, A4, A5, A6. The problem gives:
A2 = 50°, A3 = x + 25, A4 = 2x, A5 = angle 1.

With three lines through a point the opposite angles are equal, so
A1 = A4 = 2x, A2 = A5, A3 = A6.

Thus angle 1 = A5 = A2 = 50°.

Also A1 + A2 + A3 = 180° (sum of three consecutive sectors),
so 2x + 50 + (x + 25) = 180
=> 3x + 75 = 180
=> 3x = 105
=> x = 35.

Now substitute:
x + 25 = 60° and 2x = 70°.

The triangle formed by s, t, and m has angles
angle 1 = 50°, angle 2 = 60°, angle 3 = 70°.