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Two adjacent angles of a parallelogram have equal measure. Find the measure of each of the angles of the parallelogram.
Given: Two adjacent angles of a parallelogram have equal measure.
To find: Here we have to find the measure of each of the angles of the parallelogram.
Solution:
Let PQRS be a parallelogram;
Two adjacent angles of a parallelogram have equal measure. So,
∠P = ∠Q
Now,
Sum of adjacent angles of a parallelogram = 180°
∠P $+$ ∠Q = 180°
2∠P = 180°
P = 90°
Also,
90° $+$ ∠Q = 180°
∠Q = 180° $-$ 90°
∠Q = 90°
So,
∠P = ∠R = 90°
∠Q = ∠S = 90°
So, all the angles of parallelogram are equal to 90°.
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