Answer:
∠ C = 84°
Explanation:
A quadrilateral inscribed in a circle is a cyclic quadrilateral.
the opposite angles sum to 180° , that is
∠ A + ∠ C = 180 , then
x² + 60 + 8x + 36 = 180
x² + 8x + 96 = 180 ( subtract 180 from both sides )
x² + 8x - 84 = 0 ← in standard form
(x + 14)(x - 6) = 0 ← in factored form
equate each factor to zero and solve for x
x + 14 = 0 ⇒ x = - 14
x - 6 = 0 ⇒ x = 6
x > 0 , then x = 6 , so
∠ C = 8x + 36 = 8(6) + 36 = 48 + 36 = 84°