Answer:
∠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°
