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Question
`square` ABCD is a parallelogram. The ratio of `angle`A and `angle`B of this parallelogram is 5 : 4. Find the measure of `angle`B.
Solution
Quadrilateral ABCD is a parallelogram.
Let the measure of `angle`A and `angle` B be 5xº and 4xº, respectively.
Now,
`angle` A + `angle` B = 180º ...(Adjacent angles of a parallelogram are supplementary)
∴5xº + 4xº = 180º
⇒ 9xº = 180º
⇒ xº = 20º
∴ Measure of `angle`B = 4xº = 4 × 20º = 80º
Thus, the measure of `angle`B is 80º.
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