Geometry
Ten quantitative aptitude questions, each marked as you answer.
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What is each interior angle of a regular polygon with 12 sides?
Answer and working
Answer D
Each exterior angle = 360° ÷ 12 = 30°. Interior = 180° − 30° = 150°.
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An angle is 80° more than its supplement. What is the angle?
Answer and working
Answer B
a + (a − 80) = 180, so 2a = 260 and a = 130°.
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The angles of a triangle are in the ratio 6 : 1 : 3. What is the largest angle?
Answer and working
Answer B
10 parts make 180°, so one part is 18°. The largest is 6 × 18 = 108°.
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Each exterior angle of a regular polygon is 24°. How many sides does it have?
Answer and working
Answer A
Exterior angles add up to 360°, so the number of sides = 360 ÷ 24 = 15.
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What is each interior angle of a regular polygon with 30 sides?
Answer and working
Answer C
Each exterior angle = 360° ÷ 30 = 12°. Interior = 180° − 12° = 168°.
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The angles of a triangle are in the ratio 2 : 4 : 3. What is the largest angle?
Answer and working
Answer D
9 parts make 180°, so one part is 20°. The largest is 4 × 20 = 80°.
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Each exterior angle of a regular polygon is 18°. How many sides does it have?
Answer and working
Answer B
Exterior angles add up to 360°, so the number of sides = 360 ÷ 18 = 20.
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How many diagonals does a polygon with 5 sides have?
Answer and working
Answer D
n(n − 3)/2 = 5 × 2 ÷ 2 = 5.
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The angles of a triangle are in the ratio 4 : 2 : 6. What is the largest angle?
Answer and working
Answer D
12 parts make 180°, so one part is 15°. The largest is 6 × 15 = 90°.
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Each exterior angle of a regular polygon is 24°. How many sides does it have?
Answer and working
Answer C
Exterior angles add up to 360°, so the number of sides = 360 ÷ 24 = 15.
More quantitative aptitude: Percentages, Profit, loss and discount, Simple interest, Compound interest, Ratio and proportion, Averages.