Find the measure of ? d if ? a = 5 2 x + 16 ? b = 7 2 x + 20 ? c = 3 2 x + 68 ? d = 3 2 x + 40 a) 65° b) 76° c) 95° d) 104°

∠D = 76.8°

Step-by-step explanation:

Given that

∠A = 52x +16

∠B = 72x +20

∠C = 32x + 68

∠D = 32x + 40

We will assume that x represents the same value in all cases

Given that we are working with a quadrilateral, we know that all interior angles must equate to 360°.

To solve for x then, we will combine all angle measurements and equate them to 360°.

360 = 52x + 16 + 72x + 20 + 32x + 68 + 32x +40     Combine like terms

360 = 188x + 144                  take 144 away from both sides

216 = 188x                             divide both sides by 188 to isolate x

1.15 = x

Using the equation for ∠D, we will plug 1.15 in for x

∠D = 32(1.15) + 40

∠D = 36.8 + 40

∠D = 76.8°

1. supplementary angles

2. acd and bcd

step-by-step explanation: