In the diagram above, lines K and L are parallel, and lines M and N are parallel. If b = 8, then a = ____

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In the diagram above, lines K and L are parallel, and lines M and N are parallel. If b = 8, then a = ____.

Answer: 11

The labeled angle formed by lines M and K and the supplement of the labeled angle formed by lines L and N are alternating angles. Therefore, they are congruent.

The angle labeled (10a + 5) and its supplement, which is equal to (8b + 1), total 180º: (10a + 5) + (8b + 1) = 180. If b = 8, then:

(10a + 5) + (8 × 8 + 1) = 180

10a + 70 = 180

10a = 110

a = 11