- A58°
- B64°
- C32°
- D29°
Step-by-Step Solution
bisects ∠, so . Consecutive angles of a parallelogram are supplementary, so , and bisects it: . (So )
Answer: C) 32°
ABCD is a parallelogram. The blue lines AP and BP bisect ∠A and ∠B and meet at P. ∠PBC = 58°. Find the orange angle = ∠DAP.
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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