Answer:
see explanation
Explanation:
complimentary angles , sum to 90° , then
∠ A + ∠ B = 90 ( substitute values )
x² + 40 + 2x + 42 = 90 ( simplify left side )
x² + 2x + 82 = 90 ( subtract 90 from both sides )
x² + 2x - 8 = 0 ← quadratic equation in standard form
(x + 4)(x - 2) = 0 ← in factored form
equate each factor to zero and solve for x
x + 4 = 0 ⇒ x = - 4
x - 2 = 0 ⇒ x = 2
If x = - 4 , then
∠ A = x² + 40 = (- 4)² + 40 = 16 + 40 = 56°
∠ B = 2x + 42 = 2(- 4) + 42 = - 8 + 42 = 34°
the 2 complimentary angles are 56° and 34°
If x = 2 , then
∠ A = 2² + 40 = 4 + 40 = 44°
∠ B = 2(2) + 42 = 4 + 42 = 46°
the 2 complimentary angles are 44° and 46°