Find the measure of all four angles of a parallelogram whose consecutive angles are in the ratio 1 : 3.

Given consecutive angles of a parallelogram are in the ratio 1:3
Therefore, the two consecutive angles be x and 3x.
x + 3x = 180⁰ (sum of the interior angles on the same side of the transversal is 180⁰) 4x = 180⁰ x = 45⁰ Therefore the two consecutive angles are 45⁰ and 3(45⁰) = 135⁰. Since the opposite angles of a parallelogram are equal. The measures of all four angles of a parallelogram are 45⁰, 45⁰, 135⁰ and 135⁰.