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Mathematics

In the parallelogram ABCD, ∠A : ∠B = 3 : 5. ∠C =

  1. 67.5°

  2. 112.5°

  3. 45°

  4. 135°

Rectilinear Figures

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Answer

In the parallelogram ABCD, ∠A : ∠B = 3 : 5. ∠C. Quadrilaterals, R.S. Aggarwal Mathematics Solutions ICSE Class 9.

Given the ratio ∠A : ∠B = 3 : 5.

Let ∠A = 3x and ∠B = 5x.

Sum of adjacent angles in a parallelogram = 180°.

3x + 5x = 180°

8x = 180°

x = 22.5°

In a parallelogram, opposite angles are equal.

∠C = ∠A = 3x

∠C = 3 × (22.5°)

∠C = 67.5°

Hence, option 1 is the correct option.

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