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∠C = 122°   and   ∠D = 80°

Step-by-step explanation:

This is a cyclic quadrilateral.

Definition:  A cyclic quadrilateral is a quadrilateral (a four-sided two-dimensional shape) drawn inside a circle. Every vertex of the quadrilateral must touch the circumference of the circle.

The opposite angles in a cyclic quadrilateral add up to 180°.

Therefore, ∠A + ∠C = 180°   and   ∠B + ∠D = 180°

To find the value of ∠C:

∠A + ∠C = 180

        ∠C = 180 - ∠A

        ∠C = 180 - 58

        ∠C = 122°

To find the value of ∠D, first find the value of y:

              ∠B + ∠D = 180

(3y + 4) + (2y + 16) = 180

                5y + 20 = 180

                        5y = 180 - 20 = 160

                         y = 160 ÷ 5 = 32

Therefore, y = 32

To find ∠D, substitute found value of y into the expression for ∠D:

∠D = 2y + 16

∠D = 2 x 32 + 16

∠D = 80°

a² + b²= c²

24² + 7² = c²

c= 25