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If one of the angles of a parallelogram is 30° less than twice the smallest angle. Then the largest angle of parallelogram is ____.

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Detailed Solution

If one of the angles of a parallelogram is 30° less than twice the smallest angle. Then the largest angle of parallelogram is 110

o

.
Let ABCD be the given parallelogram.
Let x

o

be the measurement of smallest angle then

2 x − 30 °

is the measurement of the largest angle.
We know that adjacent angles of a parallelogram are supplementary.

∠ A + ∠ B = 18 0 °

Therefore,

x + 2 x − 3 0 ° = 18 0 ° 3 x = 21 0 ° x = 7 0 °

Substituting the value of x in

2 x − 30 °

we get,

.
Hence, the measurement of the largest angle of the given parallelogram is

11 0 °

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