Quadrilateral ABCD is inscribed in a circle such that m∠A=(x2+50)∘ and m∠C=(12x+45)∘ .What is m∠C ?Enter your answer in the box.plz explain what was done to get the answer

Answer: 105 degrees

Explanation: In a quadrilateral that is inscribed in a circle, the opposite angles are supplementary. Since angle A and angle C are opposite angles, they are supplementary. In terms of equation,

[tex]m \angle A + m \angle C = 180^{\circ} \\ \indent (x^2+50)^{\circ} + (12x+45)^{\circ} = 180^{\circ} \\ \indent (x^2 + 12x + 95)^{\circ} = 180^{\circ} \\ \indent x^2 + 12x + 95 = 180 \\ \indent x^2 + 12x - 85 = 0 \\ \indent (x - 5)(x + 17) = 0 \\ \indent \boxed{x = 5 \text{ or } x = -17}[/tex]

Note that if x = -17, 

[tex]m \angle C = 12x+45 \\ \indent = 12(-17) + 45 \\ \indent m \angle C = -159[/tex]

which is not valid because angle measure is not negative.

So, x = 5. Hence, 

[tex]m \angle C = (12x+45)^{\circ} \\ \indent = (12(5) +45)^{\circ} \\ \indent \boxed{m \angle C = 105^{\circ}}[/tex]