Geometry Questions with Solutions

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1.A parallelogram ABCD has sides AB = 24 cm and AD = 16 cm. The distance between the sides AB and DC is 10 cm. Find the distance between the sides AD and BC.
(a) 15 cm
(b) 18 cm
(c) 16 cm
(d) 9 cm

Solution :

 

2.The sum of all the interior angles of a regular polygon is four times of the sum of its exterior angles. The polygon is:
(a) Hexagon
(b) Triangle
(c) Decagon
(d) Nonagon

Ans.(c)
Sol. Sum of all exterior angles = 360°
Sum of interior angles = 4 × 360°
= 1440°
∴ 1440° = (n – 2)180°
⇒ n = 10 (number of sides)

3.Difference between the interior and exterior angles of regular polygon is 60°. The number of sides in the polygon is:
(a) 5
(b) 6
(c) 8
(d) 9

Ans.(b)
Sol. Go through options, Exterior angle
=(360°)/6=60°
Interior angle = 180° – 60° = 120°

Difference between interior angle and exterior angle = 120° – 60° = 60°

4.The ratio for the measure of an angle of a regular nonagon to the measure of its exterior angle is:
(a) 3 : 5
(b) 5 : 2
(c) 7 : 2
(d) 4 : 5

Ans.(c)
Sol. Exterior angle =(360°)/9=40°
Interior angle = 180° – 40° = 140°

∴ Interior angle: exterior angle = 140° : 40 = 7: 2

5.In the given figure, ABCD is a square. A line segment DX cuts the side BC at X and the diagonal AC at O such that ∠COD=105° and ∠OXC=x. The value of x is:

(a) 40°
(b) 60°
(c) 80°
(d) 85°

Ans.(b)
Sol. ∠OCX=45°
∠COD+∠COX=180°
⇒ ∠COX=180°-∠COD=180°-105°=75°
In ∆OCX
∠OCX+∠COX+∠OXC=180°
⇒ 45°+75°+∠OXC=180°
⇒ ∠OXC=180°-120°=60°
⇒ x = 60°

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