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Chapter 3: Q6 (page 80)

Assume that a鈭�band c鈭�d.

If m鈭�7=x, then m鈭�12=?炉and m鈭�6=?炉

Short Answer

Expert verified

Measurement of angles are:m鈭�12=x,andm鈭�6=180鈭�x

Step by step solution

01

Step 1. Observations from figure

  • ais transversal to parallel linescandd
  • bis transversal to parallel linescandd
  • cis transversal to parallel linesaandb
  • dis transversal to parallel linesaandb
02

Step 2. Find m angle 12

鈭�7and鈭�12forms a pair of alternate interior angles Theorem 3-2: If two parallel lines are cut by a transversal then the alternate interior angles are congruent.

鈭�12鈮�鈭�7m鈭�12=m鈭�7

Thus,m鈭�12=x

03

Step 3. Find m angle 6

鈭�7and鈭�12forms a pair of same-side interior angles Theorem 3-3: If two parallel lines are cut by a transversal then the same-side interior angles are supplementary.

role="math" localid="1637740498726" m鈭�6+m鈭�7=180m鈭�6+x=180m鈭�6=180鈭�x

Thus,m鈭�6=180鈭�x

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