Find the measure of ∠D if, ∠A = 52x + 16, ∠B = 72x + 20, ∠C = 32x + 68, ∠D = 32x + 40

Solution:

We will be using the angle sum property of quadrilaterals.

As we know that the sum of all interior angles of a quadrilateral is 360°.

∠A + ∠B + ∠C + ∠D= 360°.

(52x + 16) + (72x + 20) + ( 32x + 68) + (32x + 40) = 360°

By separating the like terms and adding them, we get

188 x + 144 = 360°

188 x = 360° - 144 = 216°

x = 216°/188

x = 1.1489°

∠D = 32x + 40

∠D = 32 (1.1489°) + 40

∠D = 36. 765° + 40

∠D = 76.765°

Hence, the measure of ∠D is  76.765°.

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Find the measure of ∠D if, ∠A = 52x + 16, ∠B = 72x + 20, ∠C = 32x + 68, ∠D = 32x + 40

Summary:

By using the angle sum property of quadrilateral, we get the measure of angle ∠D is 76.765°.