Question

Help heaven!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answer 1

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°

Answer 2

1. 148
2. 133
3. 140
4. 88
5. idk