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Step-by-step explanation:

m∠4 + m∠7 = 180    (Adjacent Angles of a parallelogram)

Given that m∠4 = x + 45, m∠7 = x² + 45

x + 45 + x² + 45 = 180

x² + x + 90 = 180

x² + x = 180 - 90

x² + x = 90

x² + x - 90 = 0

Using mid-term break formula

x² + 10x - 9x - 90 = 0

x(x+10) - 9(x+10) = 0

(x - 9)(x + 10) = 0

Either,

x-9 = 0       OR      x+10 = 0

x = 9          OR        x = -10

Now,

m < 7 = x² + 45

For x = 9

m < 7 = (9)² + 45

m < 7 = 81 + 45

For x = -10

m < 7 = (-10)² + 45

m < 7 = 100 + 45

Hope this helped!

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step-by-step explanation:

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step-by-step explanation:

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