Please help me, I'm really confused. Given that a ∥ b and m∠6 is 1/8 of m∠4, find m∠4 and m∠6.

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Explanation:

Finish the Given statement, make use of the relationships of angles and parallel lines, then finish the algebra.

__

2. m∠6 = (1/8)m∠4 . . . . Given

3. m∠6 + m∠4 = 180° . . . . 3. same-side interior angles are supplementary

4. m∠6 + 8·m∠6 = 180° . . . . 4. Substitution (from 2, above: 8·m∠6 = m∠4)

Here is the "algebra" that gets you to line 5:

4a. 9m∠6 = 180° . . . collect terms

4b. m∠6 = 20° . . . . . divide by 9

4c. m∠4 = 8·20° = 160° . . . use the same relation as in step 4

5. m∠6 = 20°, m∠4 = 160° . . . . Algebra

m∠6=1/8m∠4

m∠6+m∠4=180°                S.S int. of parallel lines

m∠6+8·m∠4=180°

m∠6=20° m∠4=160°

M



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