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If an angle of a parallelogram is two-third of its adjacent angle, find the angles of the parallelogram.

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83 °, 97 °, 83 °, 97 °

72 °, 108 °, 72 °, 108 °

70 °, 110 °, 70 °, 110 °

100 °, 80 °, 100 °, 80 °

answer is D.

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Detailed Solution

Given that,
An angle of a parallelogram is two-third of its adjacent angle.
Let us consider one adjacent angle is

x

.
And, the other adjacent angle is

2 x ° 3

.
As we know that the sum of adjacent angles in a parallelogram is

180 °

Measures of another adjacent angle =

180 ° − 108 ° = 72 °

.
As we know that the opposite angles in a parallelogram are equal.

∴

The other two angles are also given by 108

°

and 72

° .

So, the measures of each angle are

72 °, 72 °, 108 °, 108 °

.
Hence, the correct option is 4.

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