Problema Solution
One angle of a parallelogram is 12 degrees less than twice the measure of the angle next to it. The sum of the measures of the angles is 180 degrees. Find the measure of the adjacent angles of the parallelogram. The smaller angle measurement is ? degrees. The larger angle measures ? degrees.
Answer provided by our tutors
Let the smaller angle be x degrees.
Let the larger angle be y degrees.
One angle of a parallelogram is 12 degrees less than twice the measure of the angle next to it:
2y - x = 12
or, x = 2y - 12
Also, for adjacent angles of a prallelogram:
x + y = 180
Substituting value of x from above
2y - 12 + y = 180
3y - 12 = 180
3y = 192
y = 64
ALso, x = 2y - 12 = 2*64 - 12 = 128 - 12 = 116