Ncert Solutions For Class 7 Maths Ex 5.2

Ncert Solutions For Class 7 Maths Chapter 5 Ex 5.2

Q1: Describe the property that is used in each of the following statements:

(i)If a||b,then1=5..

(ii)If 4=6,thena||b.

(iii)If 4+5+180,thena||b.

ex5.2 q1

Ans:

(i)Given, a||b, then 1=5 [Corresponding angles]

If two parallel lines are cut by a transversal, each pair of corresponding angles are equal in measure.

(ii) Given, 4=6, then a||b [Alternate angles]

When a transversal cuts two lines such that pairs of alternate interior angles are equal, the lines have to be parallel.

(iii)Given, 4+5=180, then a||b [Co-interior angles]

When a transversal cuts two lines, such that pairs of interior angles on the same side of transversal are supplementary, the lines have to be parallel.

 

Q2: In the given figure, identify:

(i)The pairs of corresponding angles.

(ii)The pairs of alternate interior angles.

(iii)The pairs of interior angles on the same side of the transversal.

(iv)The vertically opposite angles.

ex 5.2 q2

Ans:

(i)The pairs of corresponding angles:

1,5;2,6;4,8and3,7

(ii)The pairs of alternate interior angles are:

3,5and2,8

(iii)The pair of interior angles on the same side of the transversal:

3,8and2,5

(iv)The vertically opposite angles are:

1,3;2,4;6,8and5,7

 

Q3: In the adjoining figure, p||q. Find the unknown angles.

ex 5.2 q3

Ans: Given, p||q and cut by a transversal line.

 because125+e=180    [Linear Pair]

 therefore1e=180125=55  ……(1)

Now e=f=55 [Vertically opposite angles]

Also a=f=55   [Alternate interior angles]

a+b=180   [Linear pair]

55+b=180  [From equation (1)]

b=18055=125

Now a=c=55 and b=d=125   [Vertically opposite angles]

Thus, a=55,b=125,c=55,d=125,e=55andf=55

 

Q4: Find the values of x in each of the following figures if l||m

Ans:

ex5.2 q4

(i)Given, l||m and t is transversal line.

 therefore Interior vertically opposite angle between lines l and t=110

 therefore110+x=180    [Supplementary angles]

x=180110=70

(ii)Given, l||m and t is transversal line.

x+2x=1803x=180[Interioroppositeangles]x=1803=60

(iii)Given, l||m and a||b.

x=100 [Corresponding angles]

 

Q5: In the given figure, the arms of two angles are parallel. If ABC=70, then find:

(i) DGC

(II) DEF

ex5.2 q5

Ans:

(i) From the figure ABDE and BC is a transversal line and ABC=70

 becauseABC=DGC     (corresponding angles)

DGC=70               ………(i)

 

(ii)  From the figure BCDE and DE is a transversal line and DGC=70

 becauseDGC=DEF     (corresponding angles)

DGC=70               ………(i)

 

Q6: In the given figure below, decide whether l is parallel to m.

Ans:

ex 5.2 q6

(i) 126+44=170

Here lm this condition holds false, because the sum of interior opposite angles are not equal to 180.

 

(ii) 75+75=150

Here lm this condition holds false, because the sum of interior opposite angles are not equal to 180.

 

(iii) 57+123=180

Here lm this condition holds true, because the sum of interior opposite angles are equal to 180.

 

(iv) 98+72=170

Here lm this condition holds false, because the sum of interior opposite angles are not equal to 180.