Asked by D4VD

xplaining an Angle Measure
Carmen is planning rail lines for a new train station. Help her find mes002-1.jpg1. Explain how you found that solution.
Parallel lines a and b are cut by transversal t to form 8 angles. Clockwise from top left, the angles formed with line a are blank, 17 degrees, 2, blank; with line b are 1, blank, blank, blank.
m∠1 = 163°.

Explanation:
- At line a, the top-right angle is 17°. Its vertical opposite (bottom-left at the same intersection) is also 17°.
- The top-left angle at line a is a linear pair with that 17°, so top-left = 180° − 17° = 163°. (That also makes angle 2 = 163°, since angle 2 is vertical to that top-left.)
- Because lines a and b are parallel, corresponding angles made by the transversal are equal. The top-left angle at line b (angle 1) corresponds to the top-left angle at line a, so m∠1 = 163°.
Sample response: Angle 2 is a supplementary angle with 17°, so m∠2 = 163°. Since ∠1 and ∠2 are alternate interior angles of parallel lines, they are congruent, and the m ∠1 = m ∠2. Thus, m∠1 = 163°.


Check all that you included in your response.
Angle2 and the angle marked 17º are supplementary angles.
mAngle2 + 17º = 180º
mAngle2 = 163º
Angle1 and Angle2 are alternate interior angles of parallel lines.
m Angle1 = m Angle2
mAngle1 = 163º

All Answers 1

Answered by GPT-5 mini AI
m∠1 = 163°.

Explanation / steps:
- Angle2 and the angle marked 17º are supplementary angles.
- m∠2 + 17º = 180º
- m∠2 = 163º
- Angle1 and Angle2 are alternate interior angles of parallel lines.
- m∠1 = m∠2
- m∠1 = 163º