Practice Questions
Concept Explanation
A polygon is a closed plane figure with straight sides. A regular polygon has equal sides and equal angles.
Key Formulas
- Sum of interior angles = (n − 2) × 180°
- Each interior angle (regular n-gon) = (n − 2) × 180° / n
- Each exterior angle (regular n-gon) = 360° / n
- Number of diagonals = n(n − 3)/2
Example
Regular hexagon (n = 6): each exterior angle = 360°/6 = 60°.
Common Trap
Interior and exterior angles at a vertex are supplementary (sum to 180°) only for a single vertex on a convex polygon.
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Q1 EasySum of interior angles of a pentagon is:ExplanationFor n = 5: sum = (5 − 2) × 180° = 3 × 180° = 540°. Hence the answer is 540°.
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Q2 EasySum of interior angles of a quadrilateral is:Explanation(4 − 2) × 180° = 360°. Hence the answer is 360°.
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Q3 EasyEach exterior angle of a regular hexagon is:ExplanationRegular hexagon: each exterior = 360°/6 = 60°. Hence the answer is 60°.
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Q4 EasyEach exterior angle of regular pentagon is:Explanation360°/5 = 72°. Hence the answer is 72°.
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Q5 EasyExterior angles of any convex polygon sum to:ExplanationSum of exterior angles (one at each vertex) = 360° for any convex polygon. Hence the answer is 360°.
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Q6 MediumNumber of diagonals in an octagon is:ExplanationDiagonals = n(n − 3)/2 = 8 × 5 / 2 = 20. Hence the answer is 20.
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Q7 MediumDiagonals in a hexagon equal:Explanation6 × 3 / 2 = 9. Hence the answer is 9.
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Q8 MediumEach interior angle of a regular decagon is:ExplanationInterior = (10 − 2) × 180°/10 = 144°. Hence the answer is 144°.
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Q9 MediumSum of interior angles of nonagon:Explanation(9 − 2) × 180° = 1260°. Hence the answer is 1260°.
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Q10 MediumEach interior angle of regular octagon:Explanation(8 − 2) × 180°/8 = 135°. Hence the answer is 135°.
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Q11 MediumIf each exterior angle of a regular polygon is 40°, number of sides is:Explanationn = 360°/40° = 9. Hence the answer is 9.
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Q12 HardRegular polygon has interior angle 150°. Sides:ExplanationExterior = 30°, n = 360/30 = 12. Hence the answer is 12.
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Q13 HardPolygon has 15 diagonals. Number of sides:Explanationn(n − 3)/2 = 15 ⇒ n(n − 3) = 30 ⇒ n = 6. Hence the answer is 6.
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Q14 HardSum of interior angles of a heptagon is:Explanationn = 7: sum = (7 − 2) × 180° = 900°. Hence the answer is 900°.
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DS1 Easy
How many sides does the regular polygon have?
Statement IEach exterior angle is 30°.
Statement IIEach interior angle is 150°.
ExplanationStatement I: n = 360/30 = 12. Statement II: exterior = 30°, n = 12. Each alone sufficient. Answer: D. -
DS2 Easy
What is the sum of interior angles of the polygon?
Statement IIt is a hexagon.
Statement IIIt has 6 sides.
ExplanationBoth state n = 6, sum = 720°. Each alone sufficient. Answer: D.
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DS3 Easy
How many diagonals does the polygon have?
Statement IIt has 8 sides.
Statement IIIt is an octagon.
ExplanationBoth give n = 8, diagonals = 20. Each alone sufficient. Answer: D. -
DS4 Medium
What is each interior angle of the regular polygon?
Statement IIt has 10 sides.
Statement IIEach exterior angle is 36°.
ExplanationStatement I: (8 × 180)/10 = 144°. Statement II: interior = 180 − 36 = 144°. Each alone sufficient. Answer: D.