Lines b and c are parallel. what is the measure of angle 6?

∠6 = 54°

Step-by-step explanation:

Since b and c are parallel lines, then

∠8 = 13x + 9 ( alternate exterior angle ) and

∠6 = 5x + 9 ( vertical angles )

∠6 and ∠8 form a straight angle and are supplementary, thus

13x + 9 + 5x + 9 = 180, that is

18x + 18 = 180 ( subtract 18 from both sides )

18x = 162 ( divide both sides by 18 )

x = 9

Hence

∠6 = 5x + 9 = (5 × 9) + 9 = 45 + 9 = 54°

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