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If an Angle of a Parallelogram is Two-third of Its Adjacent Angle, the Smallest Angle of the Parallelogram is - Mathematics

MCQ

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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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 13 Quadrilaterals
Q 19 | Page 72
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