Lines and Angles - Test Questions

Question 11

Question:   Two lines 'l', 'm' are perpendicular to the lines 'n', 'p'. If 'n' and 'p' intersect, prove that 'l' and 'm' must also intersect.

Answer:   
l ^ 'n' and 'm' ^ 'p' [given]
Let 'n' and 'p' intersect at 'A'

' l' and 'm' intersect.

Let us assume that 'l' and 'm' do not intersect. Then 'l' must be parallel to 'm'.
But l ^ n [given]
\m ^ n ..... (i)
now m ^ p ..... (ii)
from (i) and (ii) we conclude that n||p.
But it is given that 'n' and 'p' are intersecting lines. So our assumption that 'l' and 'm' do not intersect is wrong.
Hence 'l' and 'm' intersect.

Question 12

Question:   In the given figure 'm' and 'n' are two plane mirrors parallel to

Answer:   
m||n [given]

Question 13

Question:  

Answer:   
(Angle sum property)

Question 14

Question:   The sum of two angles of a triangle is 80^o and their difference is 20^o. Find all the angles of the triangle.

Answer:    Let the two angles of the triangle be x^o and y^o.
Then x^o+ y^o= 80^o ...(i)
x^o- y^o= 20^o ...(ii)
From equations (i) + (ii) we get 2x^o= 100^o

x^o= 50^o
Substituting x^o= 50^o in (i)
x^o+ y^o= 80^o

50^o+ y^o= 80^o
y^o = 80^o- 50^o
y^o = 30^o
The two angles of the triangle are 50^o and 30^o.
The third angle = 180^o - (50^o +30^o) (sum of angles in a triangle is 180^o)
= 180^o - 80^o
= 100^o

Question 15

Question:  

Answer:   
[angle sum property]


...(i)




...(ii)

Question 16

Question:  

Answer:   





















Thus the three angles are

Question 17

Question:   An exterior angle of a triangle is 110^o and one of the interior opposite angles is 30^o. Find the other two angles of the triangle.

Answer:   



= 80^o




= 70^o

Question 18

Question:  

Answer:   





[ Sum of angle of a triangle = 180^o]

Question 19

Question:  

Answer:   








Adding (i), (ii) and (iii)



=360^o

Question 20

Question:  

Answer:   











Multiplying both sides by 2.

Subtracting (i) from (ii)