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

To find the measure of angle D, we first need to determine the value of x using the given angles A, B, C, and D.

In any quadrilateral, the sum of the interior angles is always 360 degrees. Therefore, we can set up the equation:

Angle A + Angle B + Angle C + Angle D = 360

Substituting the expressions for the angles, we have:

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

Now, combine all the terms:

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

(188x) + (144) = 360

Next, we will isolate 188x:

188x = 360 – 144

188x = 216

Now, solve for x:

x = 216 / 188

x = 1.14893617021 (approximately).

Now that we have the value of x, we can find angle D:

Substituting x back into the equation for angle D:

Angle D = 32x + 40

Angle D ≈ 32(1.14893617021) + 40

Angle D ≈ 36.75 + 40

Angle D ≈ 76.75 degrees (approximately).

Therefore, the measure of angle D is approximately 76.75 degrees.