Question
In a cyclic quadrilateral ABCD , AB || CD and ∠ B = 65° , find the remaining angles.
✓
Answer
∠ B = 65°( given)
∠ B + ∠ D = 180 (Opposite angles of a cydic quadrilateral)
65 + ∠ D = 180
∠ D = 115
Also, AB || CD
∴ ∠ B + ∠ C = 180 (Sum of angles on same side of transversal)
∠ C = 180 - 65 = 115
Again, ∠ A+ ∠ C = 180° (Opposite angles of a cyclic quadrilateral
∠ A = 180 - 115 = 65°
∠ B + ∠ D = 180 (Opposite angles of a cydic quadrilateral)
65 + ∠ D = 180
∠ D = 115
Also, AB || CD
∴ ∠ B + ∠ C = 180 (Sum of angles on same side of transversal)
∠ C = 180 - 65 = 115
Again, ∠ A+ ∠ C = 180° (Opposite angles of a cyclic quadrilateral
∠ A = 180 - 115 = 65°
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