Chapter 2: Geometry

Solution:-

(A) 10

From the question it is given that, number of lines passing through five points.

We know that, we need tow points to form a line.

Therefore, number of lines passing through five points = 5 × 2

= 10

Solution:-

(D) 14

From the formula, diagonal = n(n – 3)/2

Where n = number of sides in a polygon.

There are 7 sides in a heptagon.

So, d = 7(7 – 3)/2

= 7(4)/2

= 28/2

= 14

Solution:-

(B) 10

From the figure, number of line segments are, AB, AC, AD, AE, BC, BD, BE, CD, CE, DE.

Therefore, there are 10 line segments in the given figure.

Solution:-

(B) 270°, 90°

We know that, measure of complete angle of clock is 360^o.

From the figure, we can say that angle at 2 = (9/12) × 360^o= 270^o

Then, angle at 1= 360^o – 270^o

= 90^o

Therefore, measures of the two angles between hour and minute hands of a clock at 9 O’ clock are 270^o and 90^o.

Solution:-

(B) 7½

We know that, bicycle wheel is in circular shape.

So, total angle of wheel is 360^o.

From the question it is given that bicycle wheel has 48 spokes.

Then, the angle between a pair of two consecutive spokes is = 360^o/48

= 7.5

= 7½

Solution:-

(B) ∠ZXY

Solution:-

(B) 45^o

As per the condition given the question, point A is shifted to point B along the ray PX such that PB = 2PA.

So, by shifting the point ‘A’ there is no change at the point ‘P’.

Therefore, the measure of ∠BPY is 45^o.

Solution:-

(D) 6

From the above figure,

Angle are, ∠POS, ∠QOS, ∠ROS, ∠POQ, ∠QOR, ∠ROS.

Therefore, the number of angles formed is 6.

Solution:-

(c) 4

Obtuse angle is defined as an angle formed greater than 90^o and less than 180^o.

From the above figure,

Angle are, ∠ROP = ∠ROQ + ∠QOP

= 65^O + 30^O

= 95^O

∠SOP = ∠ROQ + ∠QOP + ∠SOR

= 65^O + 30^O + 45^O

= 140^O

∠SOQ = ∠SOR + ∠ROQ

= 45^O + 65^O

= 110^O

∠TOQ = ∠TOS + ∠SOR + ∠ROQ

= 20^O + 45^O + 65^O

= 130^O

Therefore, the number of the obtuse angle formed is 4.

Solution:-

(C) 13

By observing the above figure, there are 13 triangles.

ΔPVR, ΔPSQ, ΔSQU, ΔSQT, ΔTQU, ΔQUR, ΔVSU, ΔVST, ΔVTU, ΔPQV, ΔRQV, ΔVSQ, ΔVUQ