1. QUESTIONS ON POLYGONS IN APTITUDE TESTS by : DR. T.K. JAIN AFTERSCHO ☺ OL centre for social entrepreneurship sivakamu veterinary hospital road bikaner 334001 rajasthan, india www.afterschoool.tk mobile : 91+9414430763

2. How many diagonals can be there is a regular hexagon? Formula = n (n-3) / 2 = 6(6-3) / 2 = 9 diagonals answer

3. How many sides are there in a convex polygon having 27 diagonals? 27= n(n-3) / 2 n^2 -3n -54 =0 n^2 – 9n+6n-54 (n-9) (n+6) thus answer is 9

4. Exterior angle of a regular polygon is 1/3 rd of interior angle. How many sides are there? Let us assume interior angle = 3, ext. Angle =1, thus interior angle = 3/4*180 = 135 fomula = (n-2) * 180/n = 135 n-2 = 3/4n, 1/4n = 2, n = 8 or ext. Angle = 45, divide 360/45 = 8

5. ABCDE is regular pentagon, diagonal AD divides angle CDE in two parts. Find the ratio of angles ADE to ADC Exterior angle = 360 / 5 = 72, interior angle = 108 make a triangle, remaining two angles will be 36 each. Thus the ADE is 36 and ADC is 72 (remaining). Thus their ratio is 1:2. answer

6. The difference between exterior angle of (n-1) sided regular polygon and exterior angle of (n+2) regular polygon is 6 degree, what is n? Try and find. 12 and 15 give you exterior angles of 30 and 24, with difference of 6, thus n = 13.

7. Ratio of interior angle to exterior angle of a regular polygon is 7:2, what is the number of sides? Exterior angle = 2/(2+7) * 180 = 40 number of sides = 360 / 40 = 9 answer

8. The ratio of number of sides of two regular polygons is 1:2, ratio of measures of their interior angles is 3:4, what is the number of sides? ? Hit and try 5 and 10 sides, will give you interior angles of 108 and 144, which have ratio of 3:4. answer

9. Measure of an angle X is twice its supplementary angle, find the angle X? Supplementary = which adds up to 180 degree. Thus if supplentary is W, angle X is 2W 3W = 180, W = 60 X = 120 answer

10. Two supplementary angles are in the ratio 2:3, find the angles ? 2x+3x = 5x 5X = 180, so X = 36 thus the angles are 72 and 108 degree respectively

11. A person at a distance of 10 meters from a tree finds angles of elevation of the top of tree to be 45 degree, what is the height of the tree Tan = perpendicular /base tan 45 = 1 thus height of tree is 10 meters. Answer

12. 60 meter tall tower has a shadow of 60/sqrt(3) meters in lenght. Find the elevation of Sun? perpendicular/base = 60/60/sqrt(3) = sqrt(3) thus it should be tan 60 degree. Answer

13. 400000 to be paid on monthly instalments in 3 years, rate 15%, payment in the beginning of the month, find instalment Present value=annuity/rate (1+rate)(1-(1+rate)^-n rate = 15/(12*100) = .0125 400000=a/.0125 * (1.0125)(1-(1.0125)^-36) =13695 answer

14. Rishi buys a TV in 48000 on instalments. 8000Downpayment and remaining in 15 instalments. Rate : 18%. find annual instalment Present value=annuity/rate (1+rate)(1-(1+rate)^-n rate = 18/(100) = .18 40000=a/.18 * (1-(1.18)^-15) = 7856 answer

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