# SCC Education

## 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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