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Geometry question help

Geometry question help-example-1

1 Answer

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Answer:

x = 15 ( option 4 )

Explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ ACD is an exterior angle of the triangle , then

∠ ACD = ∠ A + ∠ B ( substitute values )

9x + 27 = x² - 6x + 2x - 3 ( simplify right side )

9x + 27 = x² - 4x - 3 ( subtract 9x + 27 from both sides )

0 = x² - 13x - 30 ← standard form of quadratic equation )

0 = (x - 15)(x + 2) ← factored form

equate each factor to zero and solve for x

x - 15 = 0 ⇒ x = 15

x + 2 = 0 ⇒ x = - 2

However, x must be greater than zero , then x = 15

User Daniel Eberl
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