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?
+240 Because a quadrilateral angles sum up to 360 degrees, A, B, C, and D must sum to 360.
Since it's a arithmetic sequence with B being 72, we can write them as
A, B, C, D
72-x, 72, 72+x, 72+2x
Add them all up to get, 288+2x = 360. Simplify to get x = 36, and angle D was equal to 72 + 2x, so angle D is 144 degrees.
+876 Let $\angle{A} = x.$
Let the change in angles be $n.$
We have: $x+(x+n)+(x+2n)+(x+3n) = 360$
$x+n = 72$
We want to find $x+3n.$
Rewrite first equation: $3x+5n + 72 = 360$
$3x + 5n = 288$
Rewrite third equation: $3x + 3n = 216$
$2n = 72$
$3n = \frac{3}{2} \cdot 72 = 108$
$n = 36$
$x + 36 = 72$
$x = 36$
$x + 3n = 36 + 108 = \boxed{144}$
