The figure is shown below:
In the given figure,
Line YQ bisect ∠ZYP.
∴ ∠QYP = ∠ZYQ = x (let) .........(1)
From figure,
⇒ ∠XYZ + ∠ZYQ + ∠QYP = 180° [Linear pairs]
⇒ 64° + x + x = 180° [From equation (1)]
⇒ 64° + 2x = 180°
⇒ 2x = 180° - 64°
⇒ 2x = 116°
⇒ x =
⇒ x = 58°.
⇒ ∠ZYQ = ∠QYP = x = 58°
Reflex ∠QYP = 360° - ∠QYP = 360° - 58° = 302°.
From figure,
⇒ ∠XYQ = ∠XYZ + ∠ZYQ
= 64° + 58°
= 122°.
Hence, ∠XYQ = 122° and Reflex ∠QYP = 302°.
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CBSE Class IX | Academic Year 2026-2027
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Mathematics | Lines and AnglesWeb Content • Interactive Notes
Lines and Angles — Interactive Study Guide
Angle Pair Cheat Sheet
| Pair | Relationship | Condition |
|---|---|---|
| Complementary | Sum = 90° | Any two angles |
| Supplementary | Sum = 180° | Any two angles |
| Linear Pair | Sum = 180° | Adjacent + on a line |
| Vertically Opposite | Equal | Intersecting lines |
| Corresponding | Equal | Parallel lines + transversal |
| Alternate Interior | Equal | Parallel lines + transversal |
| Co-interior | Sum = 180° | Parallel lines + transversal |
Triangle Angle Facts
∠A + ∠B + ∠C = 180° (angle sum property)
Exterior angle = sum of remote interior angles
Quick Self-Check
- Two parallel lines cut by a transversal: one angle is 72°. Find all 8 angles. (72°, 108° alternating)
- In ΔABC, ∠A = 45°, ∠B = 65°. Find ∠C. (70°)
- An exterior angle of a triangle is 130°. One non-adjacent interior angle is 50°. Find the other. (80°)