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Mathematics

If one angle of a parallelogram is 30° less than twice the smallest angle, then measure of each angle will be :

  1. 60°, 80°, 80°, 140°

  2. 70°, 110°, 70°, 110°

  3. 60°, 120°, 60°, 120°

  4. 75°, 105°, 75°, 105°

Rectilinear Figures

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Answer

Let the smallest angle of the parallelogram be denoted as x.

Given,

One angle of a parallelogram is 30° less than twice the smallest angle = 2x - 30°.

In a parallelogram, consecutive angles are supplementary and opposite angles are equal.

x + 2x - 30° = 180°

3x - 30° = 180°

3x = 180° + 30°

3x = 210°

x = 70°.

The two smaller angles are both 70°.

The two larger angles are both 2(70°) - 30° = 110°.

Hence, option 2 is the correct option.

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