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Question
If an angle of a parallelogram is two-third of its adjacent angle, the smallest angle of the parallelogram is
Options
108°
54°
72°
81°
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Solution
Let one of the angle of the parallelogram as x°
Then the adjacent angle becomes `2/3 x°`
We know that the sum of adjacent angles of the parallelogram is supplementary.
Therefore,
`x + 2/3x = 180°`
`5/3 X = 180°`
`x = 180 (3/5)`
x = 108°
Thus, the angle adjacent to 108°
`= 2/3 (108°)`
= 72°
Therefore, the smallest angle of the parallelogram as 72°
Hence, the correct choice is (c).
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