Question

olving 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.

Using the diagram, determine which statements are true. Select all that apply.
m∠1 = 50°
m∠3 = (2x + x + 25)°
m∠2 = (x + 25)°
m∠1 + m∠2 + m∠3 = 180°
50 + 2x+ x + 25 = 180

Answer 1

Select all true:
- m∠1 = 50°
- m∠2 = (x + 25)°
- m∠1 + m∠2 + m∠3 = 180°
- 50 + 2x + x + 25 = 180

Reasoning (brief):
- At the intersection, the 50° angle and angle 1 are vertically opposite, so m∠1 = 50°.
- By parallel lines, the angle labeled (x + 25)° at the top corresponds to the triangle's angle 2, so m∠2 = x + 25°.
- Angles 1, 2, 3 are the triangle's interior angles, so their measures sum to 180°.
- Substituting m∠1 = 50°, m∠2 = x + 25°, and m∠3 = 2x gives 50 + 2x + (x + 25) = 180, i.e. 50 + 2x + x + 25 = 180.

The statement m∠3 = (2x + x + 25)° is false (m∠3 = 2x°, not the sum).