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°