- A42°
- B30°
- C72°
- D36°
Step-by-Step Solution
Consecutive angles are supplementary, so and . Since (alternate angles).
Answer: B) 30°
ABCD is a parallelogram with diagonal AC. ∠DAC = 42° and ∠ABC = 108°. Find the orange angle = ∠ACD.
Class 9QuadrilateralsGeometry — Quadrilaterals
Key idea: Special parallelograms
**Rectangle** (parallelogram + all angles 90°):
- All properties of a parallelogram.
- Diagonals are EQUAL (in addition to bisecting each other).
**Rhombus** (parallelogram + all sides equal):
- All properties of a parallelogram.
- Diagonals bisect each other AT RIGHT ANGLES.
- Diagonals also bisect the angles of the rhombus.
**Square** (rectangle + rhombus):
- All properties of both.
- Diagonals: equal, bisect at right angles, AND bisect angles.
- All properties of a parallelogram.
- Diagonals are EQUAL (in addition to bisecting each other).
**Rhombus** (parallelogram + all sides equal):
- All properties of a parallelogram.
- Diagonals bisect each other AT RIGHT ANGLES.
- Diagonals also bisect the angles of the rhombus.
**Square** (rectangle + rhombus):
- All properties of both.
- Diagonals: equal, bisect at right angles, AND bisect angles.
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