# EXERCISE – 5.2

Q1. State the property that is used in each of the following statements?

SOLUTION:-

(i) If A parallel to B, then Angle 1 = Angle 5.

(ii) If Angle 4 = Angle 6, then A parallel to B

(iii) If Angle 4 + Angle 5 = 1800, then A parallel to B.

SOLUTION:-

(i) If A parallel to B, then Angle 1 = Angle 5.

SOLUTION:-

Corresponding angles property is used in the above statement.

(ii) If Angle 4 = Angle 6 then A parallel to B .

SOLUTION:-

Alternate interior angle property is used in the above

statements

(iii) If Angle 4 + Angle 5 = 1800, then a parallel to b

SOLUTION:-

Interior angles on the same side of the transversal are supplementary.

Q2. In the adjoining 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.

(i) By observing the figure , the pairs of corresponding angles are,

Angle 1 and Angle 5 , Angle 4 and Angle 8, Angle 2 and Angle 6 , Angle 3 and Angle 7

(ii) By observing the figure , the pairs of alternate interior angle are,

Angle 2 and Angle 8 , Angle 3 and Angle 5

(iii) By observing the figure , the pairs of interior angle on the same side of the transversal are Angle 2 and Angle 5 , Angle 3 and Angle 8

(iv) By observing the figure, the vertically opposite angles are,

Angle 1 and Angle 3 , Angle 5 and Angle 7 , Angle 2 and Angle 4 , Angle 6 and Angle 8.

Q3. In the adjoining figure, p parallel to q Find the unknown angles.

SOLUTION:-

By observing the figure,

Angle d = Angle 1250    [ corresponding angles]

We know that, Linear pair is the sum of adjacent angles is 1800

Then,

= Angle e + 1250 = 1800  [ Linear pair]

= Angle e = 1800 – 1250

= Angle e = 550

From the rule of vertically opposite angles,

= Angle f =Angle e = 550

= Angle b = Angle d = 1250

By the property of corresponding angles,

Angle c = Angle f = 550

Angle a = Angle e = 550

Q4.Find the value of x in each of the following figures if l parallel m.

SOLUTION:-

(i) Let us assume other angle on the line m be Angle y.

Then,

By property of corresponding angles,

Angle y = 1100

We know that linear pair is the sum of adjacent angles is 1800

Then,

= Angle x + Angle y = 1800

= Angle x + 1100 = 1800

= Angle x = 1800 – 1100

= Angle x = 700

(ii)By the property of  corresponding angles,

Angle x = 1000

Q5.In the given figure the arms of two angles are parallel If Angle ABC = 700 then find

(i) Angle DGC

(ii) Angle DEF

SOLUTION:-

(i) Let us consider that AB parallel DG

BC is the transversal line intersecting AB and DG

By the property of corresponding angles,

Angle DGC = Angle ABC

Then,

Angle DGC = 700

(ii) Let us consider that BC parallel EF

DE is the transversal line intersecting angles,

Angle DEF = Angle DGC

Then,

Angle DEF = 700

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

SOLUTION:-

(i) Let us consider the two lines l and m

n is the transversal line intersecting l and m

We know that the sum of interior angle on the same side of the transversal is 1800

Then,

= 1260 + 440

= 1700

But, the sum of interior angle on the same side of transversal is not equal to 1800

So, line l is not parallel to line m .

(ii) Let us assume Angle x be the vertically opposite angle formed  due to the intersection of the straight line l and transversal n,

Then, Angle x = 750

Let us consider the two lines l and m

We know that the sum of interior angle on the same side of transversal is not equal to 1800

So, line l is not parallel to line m.

(iii) Let us assume Angle x be the vertically opposite angle formed due to the intersection of the straight line l and transversal line n,

Let us consider the two lines l and m ,

n is the transversal line intersecting l and m

We know that the sum of interior angles on the same side of the transversal is 1800

Then,

= 1230 + Angle x

= 1230 + 570

= 1800

The sum of interior angles on the same side of transversal is equal to 1800.

So, line l is parallel to line m.

(iv) Let us assume Angle x be the angle formed due to the intersection of the straight line l and transversal line n,

We know that linear pair is the sum of adjacent angles is equal to 1800.

= Angle x + 980 = 1800

= Angle x = 1800 –  980

= Angle x = 820

Now we consider Angle x and 720 are the corresponding angles.

For l and m to be parallel to each other, corresponding angles should be equal.

But, in the given figure corresponding angles measures 820 and 720 respectively.

Line l is not parallel to line m.