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