- A9
- B7
- C8
- D16
Step-by-Step Solution
Exterior angle = 180 − 135 = 45°. Number of sides = 360 / 45 = 8 (a regular octagon).
Answer: C) 8
How many sides does a regular polygon have if each interior angle is 135°?
Class 8Understanding QuadrilateralsQuadrilaterals
Key idea: Sum of exterior angles
**The sum of the exterior angles of any convex polygon (one at each vertex) is always 360°** — no matter how many sides.
For a regular n-gon, each exterior angle = 360°/n. So a regular quadrilateral (square) has exterior angle 360/4 = 90°. A regular pentagon: 72°. A regular hexagon: 60°.
For a regular n-gon, each exterior angle = 360°/n. So a regular quadrilateral (square) has exterior angle 360/4 = 90°. A regular pentagon: 72°. A regular hexagon: 60°.
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