Question

Two adjacent angles of a parallelogram have equal measure. Find the measure of each of the angles of the parallelogram.

Answer 1

Sum of adjacent angles = \(180°\)
\(∠ A + ∠ B = 180\degree\)
\(2∠ A = 180º (∠ A = ∠ B)\)
\(∠ A = 90\degree\)
\(∠ B = ∠ A = 90\degree \\∠ C = ∠ A = 90\degree \;(Opposite \;angles) \\∠ D = ∠ B = 90\degree \;(Opposite \;angles)\)

Thus, each angle of the parallelogram measures \(90\degree\).