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Mathematics

Assertion (A) : The adjacent angles of a parallelograms are in ratio 2 : 3 the remaining angles are 78° and 102°.

Reason (R) : Opposite angles of a parallelogram are equal.

  1. Both A and R are correct, and R is the correct explanation for A.

  2. Both A and R are correct, and R is not the correct explanation for A.

  3. Statement 1 is true, and statement 2 is false.

  4. Statement 1 is false, and statement 2 is true.

Quadrilaterals

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Answer

Given, the adjacent angles of a parallelograms are in ratio 2 : 3.

Let the adjacent angles be 2x and 3x.

We know that in a parallelogram, adjacent angles are supplementary.

⇒ 2x + 3x = 180°

⇒ 5x = 180°

⇒ x = 180°5\dfrac{180°}{5}

⇒ x = 36°

Adjacent angles = 2x = 2 x 36° = 72°

and, 3x = 3 x 36° = 108°.

Opposite angles of parallelogram are equal.

So, all angles of parallelogram are 78°, 108°, 78°, 108°.

So, assertion (A) is true.

By property,

Opposite angles of parallelogram are equal.

So, reason (R) is true.

∴ Both A and R are correct, and R is the correct explanation for A.

Hence, option 1 is the correct option.

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