Practice Questions
Concept Explanation
A polygon is a closed plane figure with straight sides. An n-sided polygon has:
- Sum of interior angles = (n − 2) × 180°
- Each interior angle (regular polygon) = (n − 2) × 180° / n
- Sum of exterior angles = 360° (any convex polygon)
Examples
Pentagon (5 sides): interior sum = 540°. Regular hexagon: each interior angle = 120°.
Common Trap
Do not use 180n for interior angle sum — the correct formula is (n − 2) × 180°.
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Q1 Easy
Sum of interior angles of a pentagon is:
Explanation(5 − 2) × 180° = 540°. -
Q2 Easy
Sum of interior angles of a hexagon is:
Explanation(6 − 2) × 180° = 720°. -
Q3 Easy
Each interior angle of a regular hexagon is:
Explanation720° / 6 = 120°. -
Q4 Medium
Each interior angle of a regular pentagon is:
Explanation540° / 5 = 108°. -
Q5 Easy
Sum of exterior angles of any convex polygon is:
ExplanationExterior angles always sum to 360°. -
Q6 Medium
Each exterior angle of a regular octagon is:
Explanation360° / 8 = 45°. -
Q7 Hard
A regular polygon has each interior angle 150°. Number of sides is:
Explanation(n − 2) × 180/n = 150 gives n = 12.
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Q8 Medium
Sum of interior angles of an octagon is:
Explanation(8 − 2) × 180° = 1080°. -
Q9 Medium
Each exterior angle of a regular decagon is:
Explanation360° / 10 = 36°. -
Q10 Medium
A regular polygon has each exterior angle 30°. It has:
Explanationn = 360° / 30° = 12 sides. -
Q11 Hard
Sum of interior angles of a heptagon (7 sides) is:
Explanation(7 − 2) × 180° = 900°. -
Q12 Hard
Each interior angle of a regular nonagon is:
Explanation(7 × 180°) / 9 = 140°. -
Q13 Hard
Number of diagonals in a hexagon is:
Explanationn(n − 3)/2 = 6 × 3/2 = 9 diagonals. -
Q14 Hard
Each interior angle of a regular polygon is 144°. Number of sides is:
ExplanationExterior = 36°, so n = 360/36 = 10.
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DS1 Easy
How many sides does the regular polygon have?
Statement IEach interior angle is 120°.
Statement IIEach exterior angle is 60°.
ExplanationEach alone: n = 360/60 = 6 sides. -
DS2 Medium
What is the sum of interior angles of the polygon?
Statement IIt has 9 sides.
Statement IIIt is a regular nonagon.
ExplanationStatement I alone: (9 − 2) × 180° = 1260°. Regularity is not needed for the sum.
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DS3 Medium
What is each interior angle of the regular polygon?
Statement IIt has 8 sides.
Statement IISum of interior angles is 1080°.
ExplanationStatement I alone: 1080/8 = 135°. Statement II alone also implies 8 sides. -
DS4 Easy
How many sides does a regular polygon have?
Statement IEach exterior angle is 24°.
Statement IIThe polygon is regular.
ExplanationStatement I alone: n = 360/24 = 15. Regularity alone does not give n.