Answer:
∠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°
