The measures of two consecutive angles in a parallelogram are in the ratio 4:11. What are the measures of the four angles of the parallelogram?

1 Answer
Feb 14, 2016

#A_1 = 48#
#A_2 = 132#
#A_3 = 48#
#A_4 = 132#

Explanation:

Consecutive angles of a parallelogram are supplementary.

Let #4x# be the measure of the smaller angle.
#=> 11x# is the measure of the larger angle.

#4x + 11x = 180#
#=> 15x = 180#

#=> x = 12#

#=> A_1 = 4x = 48#

#=> A_2 = 11x = 132#

Since we are dealing with a parallelogram, its opposite interior angles are equal.

#=> A_3 = A_1 = 48#

#=> A_4 = A_2 = 132#