Find the measure of ∠C if ∠A = 5 2 x + 30 ∠B = 7 2 x + 40 ∠C = 9 2 x + 10 ∠D = 5 2 x + 20 A) 70° B) 80° C) 90° D) 100°

D) 100°

Step-by-step 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°

Answer: greater than2