Question

Carmen is planning rail lines for a new train station. Help her find m<1. 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.

Answer 1

Answer:

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°.

Step-by-step explanation:

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Answer 2

Answer:

• m<1 =163 degrees
• 163,17,163,17 (all in degrees)

• 163,17,163,17  (all in degrees)

Step-by-step explanation:

I have reproduced and attached a diagram (in figure 1) of the problem.

For ease of understanding, I have attached a second diagram which is labelled.

On line a

17+<CBE=180 (Linear Pair Postulate)

m<2=<CBE=180-17=163 degrees

<ABG=<CBE=163 degrees (Vertically Opposite Angles)

<ABE=<GBC= 17 degrees(Vertically Opposite Angles)

On line b

m<1=<DEB=<ABG=163 degrees (Corresponding Angles)

<BEF=<GBC= 17 degrees (Corresponding Angles)

<HEF=<DEB=163 degrees  (Vertically Opposite Angles)

<DEH=<BEF=17 degrees (Vertically Opposite Angles)

Therefore:

• m<1 =163 degrees

• Clockwise from top left, the angles formed with line a are: 163 degrees, 17 degrees, m<2=163 degrees and 17 degrees.

• Clockwise from top left, the angles formed with line b are: m<1=163 degrees, 17 degrees, 163 degrees, and 17 degrees.