- A70°
- B20°
- C140°
- D110°
Step-by-Step Solution
Opposite angles of a parallelogram are equal: , so . Consecutive angles are supplementary: .
Answer: D) 110°
ABCD is a parallelogram (arrow marks show AB ∥ DC). ∠° and ∠°. Find ∠B.
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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