The measure of each angle is 65°, 65°, 115°, and 115°.
Work Step by Step
Opposite angles of a parallelogram have the same measure and the sum of the four angles is 360°. Let the non-equal angles be x and y. Hence, $2x+2y=360$ $2(x+y)=360$ $x+y=180$ The problem tells us that one angle of the parallelogram is 15° less than twice the measure of the angle next to it: $x=2y-15$ Substitute into $x+y=180$ $2y-15+y=180$ $3y=195$ $y=65°$ $x+65=180$ $x=115°$ So, the measure of each angle is 65°, 65°, 115°, and 115°. Check: $65+65+115+115=360$ And $2*65-15=115$