- A90°
- B60°
- C120°
- D45°
Step-by-Step Solution
Adjacent angles sum to 180°. Their halves sum to 90°. In the triangle formed, the angle between the bisectors = 180 − 90 = 90°.
Answer: A) 90°
In a parallelogram, the bisectors of two adjacent angles meet at a point. The angle between these two bisectors is:
Class 8Understanding QuadrilateralsQuadrilaterals
Key idea: Properties of a parallelogram
Every parallelogram has these four properties (any one of them implies the others, in fact):
1. **Opposite sides are parallel** (definition).
2. **Opposite sides are equal in length.**
3. **Opposite angles are equal.**
4. **Diagonals bisect each other** (each diagonal cuts the other into two equal halves).
Also: **consecutive angles are supplementary** (sum to 180°). So if one angle of a parallelogram is 70°, the next is 110°, the next 70°, the last 110°.
1. **Opposite sides are parallel** (definition).
2. **Opposite sides are equal in length.**
3. **Opposite angles are equal.**
4. **Diagonals bisect each other** (each diagonal cuts the other into two equal halves).
Also: **consecutive angles are supplementary** (sum to 180°). So if one angle of a parallelogram is 70°, the next is 110°, the next 70°, the last 110°.
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