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.