Answer:
D) 100°
Explanation:
From the question;
∠A = 5 2 x + 30
∠B = 7 2 x + 40
∠C = 9 2 x + 10
∠D = 5 2 x + 20
To solve this question, we first need to find the value of x and then insert it back in angle c.
The sum of angle in a 4 sided polygon is 360°
∠A + ∠B+ ∠C+ ∠D = 360°
5 2 x + 30 + 7 2 x + 40 + 9 2 x + 10 + 5 2 x + 20 = 360
We can re-arrange the equation
52 x + 72 x + 92 x + 52 x + 30 + 40 + 10 + 20 = 360
On the left hand-side of the equation, add all the x variables together and then add all the constants together.
268 x + 100 = 360
subtract 100 from both-side of the equation
268 x + 100 - 100 = 360 - 100
268 x = 260
Divide both-side of the equation by 268
268x /268 = 260/268
x = 0.97
∠A = 5 2 x + 30 = 52(0.97) + 30 = 50.44 + 30 =80.44≈ 80
∠B = 7 2 x + 40 = 72(0.97) + 40 =69.84 + 40 =109.84≈ 110
∠C = 9 2 x + 10 = 92(0.97) + 10 = 89.24 + 10 =99.24≈ 100
∠D = 5 2 x + 20 = 52(0.97) + 20 = 50.44 + 20 =70.44≈ 70
To check
∠A + ∠B+ ∠C+ ∠D = 360°
80°+ 110° + 100°+70° = 360°
Therefore ∠C =100°