The measure of angles of quadrilateral ABCD form the arithmetic sequence ∠A, ∠B, ∠C, ∠D. If the measure of angle B is \(72\) degrees what is the degree measure of angle D?
We know that the interior angle sum of quadrilateral ABCD = 360degrees.
Because we also know that angles A, B, C, D all form an arithmetic sequence, we can set a variable 'x' for the difference between the angles.
∠A = (72 - x)degrees
∠B = 72degrees
∠C = (72 + x)degrees
∠D = (72 + 2x)degrees
Angles A + B + C + D = 360degrees = 4(72) - x + x + 2x = 288 + 2x.
360 - 288 = 2x, x = 36degrees.
Since we are calculating for the degree measure of angle D, then m∠D = 72 + 2x = 144degrees.
The answer to your questions is 144 degrees.