## Quadrilateral and Parallelogram Solved Extra Questions

**Quadrilateral and Parallelogram Solved Extra Questions:-**

1. Prove that any two adjacent
angles of a parallelogram are supplementary

**Solution:**Let ABCD be a parallelogram

Then, AD ∥ BC and AB is a transversal.

Therefore, A + B = 180°

[Since, sum of the interior angles on the same side of the
transversal is 180°]

Similarly, ∠B + ∠C = 180°, ∠C + ∠D = 180° and ∠D + ∠A = 180°.

Thus, the sum of any
two adjacent angles of a parallelogram is 180°.

Hence, any two adjacent angles
of a parallelogram are supplementary

2. Two adjacent angles of a parallelogram are
as 2 : 3. Find the measure of each of its angles.

**Solution:**Let ABCD be a given parallelogram

Then, ∠A and ∠B are its adjacent angles.

Let ∠A = (2x)°
and ∠B = (3x)°.
Then, ∠A + ∠B = 180°

[Since, sum of adjacent angles of a ∥gm is 180°]
⇒ 2x + 3x =
180 ⇒ 5x = 180 ⇒ x = 36.
Therefore, ∠A = (2 ×
36)° = 72° and ∠B = (3 ×
36°) = 108°. Also, ∠B + ∠C = 180°

[Since, ∠B and ∠C are adjacent angles] = 108° + ∠C = 180°
[Since, ∠B = 108°] ∠C = (180° -
108°) = 72°. Also, ∠C + ∠D = 180° [Since, ∠C and ∠D are
adjacent angles]

72° + ∠D = 180° ⇒ ∠D = (180°
- 72°) 108°.

Therefore, ∠A = 72°, ∠B = 108°, ∠C
= 72°and ∠D = 108°.

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