Answer:
A). ∠A = 106°
B). ∠A = 133°
C). ∠B = 140°
D). ∠A = 88°
E). ∠C = 62°
Step-by-step explanation:
If a quadrilateral is inscribed in a circle then all the vertices will lie on the circle. Inscribed quadrilateral theorem states that opposite angles of this quadrilateral will supplement each other.
A) By theorem ∠A + ∠C = 180
∠A = 180 - ∠C = 180 - 74 = 106°
B). ∠A + ∠C = 180
(4x+5) + (x+15) = 180
5x+20 = 180
5x = 160 ⇒ x = 32
Therefore ∠A = (4x+15) = (4×32+15) = 133°
C). ∠C + ∠D = 180°
x + (4x-20) = 180
5x - 20 = 180
5x = 200
x = 40
Therefore ∠B = (4x-20) = (4×40-20) = 160-20 = 140°
D). ∠D + 116 = 180
∠D = X = 180-116 = 64°
∠A = (2X -40) = 2×64 - 40 = 88°
E). ∠D + ∠B = 180°
(X+20) + 3X = 180
4X +20 = 180
4X = 160 ⇒ X = 40
And ∠A + ∠C = 180
∠A = 2X + 38 = 2×40 + 38 = 118°
Therefore ∠C = 180 - ∠A = 180 - 118 = 62°
