# 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.$a||b,\; then\: \angle 1=\angle 5.$.

(ii)If 4=6,thena||b.$\angle 4=\angle 6,\, then\: a||b.$

(iii)If 4+5+180,thena||b.$\angle 4+\angle 5+180^{\circ},\, then\: a||b.$

Ans:

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

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

(ii) Given, 4=6$\angle 4=\angle 6$, then a||b$a||b$ [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$\angle 4+\angle 5=180^{\circ}$, then a||b$a||b$ [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.

Ans:

(i)The pairs of corresponding angles:

1,5;2,6;4,8and3,7$\angle 1,\angle 5;\angle 2,\angle 6;\angle 4,\angle 8 and \angle 3,\angle 7$

(ii)The pairs of alternate interior angles are:

3,5and2,8$\angle 3,\angle 5 \: and\: \angle 2,\angle 8$

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

3,8and2,5$\angle 3,\angle 8 \: and\: \angle 2,\angle 5$

(iv)The vertically opposite angles are:

1,3;2,4;6,8and5,7$\angle 1,\angle 3 ;\angle 2,\angle 4;\angle 6,\angle 8 \: and\: \angle 5,\angle 7$

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

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

because125+e=180$\ because 125^{\circ}+e=180^{\circ}$    [Linear Pair]

therefore1e=180125=55$\ therefore 1e=180^{\circ}-125^{\circ}=55^{\circ}$  ……(1)

Now e=f=55$e=f=55^{\circ}$ [Vertically opposite angles]

Also a=f=55$a=f=55^{\circ}$   [Alternate interior angles]

a+b=180$a+b=180^{\circ}$   [Linear pair]

55+b=180$\Rightarrow 55^{\circ}+b=180^{\circ}$  [From equation (1)]

b=18055=125$\Rightarrow b=180^{\circ}-55^{\circ}=125^{\circ}$

Now a=c=55$a=c=55^{\circ}$ and b=d=125$b=d=125^{\circ}$   [Vertically opposite angles]

Thus, a=55,b=125,c=55,d=125,e=55andf=55$a=55^{\circ},b=125^{\circ},c=55^{\circ},d=125^{\circ},e=55^{\circ} \: and \: f=55^{\circ}$

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

Ans:

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

therefore$\ therefore$ Interior vertically opposite angle between lines l and t=110$110^{\circ}$

therefore110+x=180$\ therefore 110^{\circ}+x=180^{\circ}$    [Supplementary angles]

x=180110=70$\Rightarrow x=180^{\circ}-110^{\circ}=70^{\circ}$

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

x+2x=1803x=180[Interioroppositeangles]x=1803=60$x+2x=180^{\circ}\\ \\ \Rightarrow 3x=180^{\circ}  [Interior \;opposite\; angles]\\ \\ \Rightarrow x=\frac{180^{\circ}}{3}=60^{\circ}$

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

x=100$x=100^{\circ}$ [Corresponding angles]

Q5: In the given figure, the arms of two angles are parallel. If ABC=70$\bigtriangleup ABC=70^{\circ}$, then find:

(i) DGC$\angle DGC$

(II) DEF$\angle DEF$

Ans:

(i) From the figure ABDE$AB\parallel DE$ and BC is a transversal line and ABC=70$\angle ABC=70^{\circ}$

becauseABC=DGC$\ because  \angle ABC=\angle DGC$     (corresponding angles)

DGC=70$∴ \angle DGC=70^{\circ}$               ………(i)

(ii)  From the figure BCDE$BC\parallel DE$ and DE is a transversal line and DGC=70$\angle DGC=70^{\circ}$

becauseDGC=DEF$\ because  \angle DGC=\angle DEF$     (corresponding angles)

DGC=70$∴ \angle DGC=70^{\circ}$               ………(i)

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

Ans:

(i) 126+44=170$126^{\circ}+44^{\circ}=170^{\circ}$

Here lm$l\parallel m$ this condition holds false, because the sum of interior opposite angles are not equal to 180$180^{\circ}$.

(ii) 75+75=150$75^{\circ}+75^{\circ}=150^{\circ}$

Here lm$l\parallel m$ this condition holds false, because the sum of interior opposite angles are not equal to 180$180^{\circ}$.

(iii) 57+123=180$57^{\circ}+123^{\circ}=180^{\circ}$

Here lm$l\parallel m$ this condition holds true, because the sum of interior opposite angles are equal to 180$180^{\circ}$.

(iv) 98+72=170$98^{\circ}+72^{\circ}=170^{\circ}$

Here lm$l\parallel m$ this condition holds false, because the sum of interior opposite angles are not equal to 180$180^{\circ}$.