Question

If m<A = 4x + 31 and m<B = 2x -7, what is the measure of each angle if they are supplementary??

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Answer 1

∠ A = 135° , ∠ B = 45°

Explanation:

supplementary angles sum to 180°

sum the angles, equate to 180 and solve for x

∠ A + ∠ B = 180° ( substitute values )

4x + 31 + 2x - 7 = 180 ( simplify left side )

6x + 24 = 180 ( subtract 24 from both sides )

6x = 156 ( divide both sides by 6 )

x = 26

Then

∠ A = 4x + 31 = 4(26) + 31 = 104 + 31 = 135°

∠ B = 2x - 7 = 2(26) - 7 = 52 - 7 = 45°