# Exercise 5.2

QUESTION 1

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

**(i) If a || b, then ∠1 = ∠5**

Sol : Corresponding angles property

**(ii) If ∠4 = ∠6 , then a || b**

Sol : Alternate interior angles property

**(iii) If ∠4 + ∠5 = 180° , then a || b**

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

QUESTION 2

**In the adjoining figure, identify**

**(i) The pairs of corresponding angles**

Sol :

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

**(ii) The pairs of alternate interior angles**

Sol :

∠2 and ∠8 , ∠3 and ∠5

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

Sol :

∠2 and ∠5 , ∠3 and ∠8

**(iv) The vertically opposite angles**

Sol :

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

QUESTION 3

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

Sol :

∠d = 125° (Corresponding angles)

∠e = 180° – 125° = 55° (Linear pair)

∠f= ∠e = 55° (Vertically opposite angles)

∠c = f = 55° (Corresponding angles)

∠a = ∠e = 55° (Corresponding angles)

∠b = ∠d = 125° (Vertically opposite angles)

QUESTION 4

Find the value of ** x** in each of the following figures if

**l || m**Sol :

(i)

∠y = 110° (Corresponding angles)

∠x + ∠y = 180° (Linear pair)

∠y = 180° – 110°

∠y = 70°

(ii)

∠x = 100° (Corresponding angles)

QUESTION 5

**In the given figure, the arms of two angles are parallel.**

If ∠ABC = 70°, then find

**(i) ∠DGC**

Sol :

(i) Consider that AB || DG and a transversal line BC is intersecting them.

∠DGC = ∠ABC (Corresponding angles)

∠DGC = 70°

**(ii) ∠DEF**

Sol :

(ii) Consider that BC || EF and a transversal line DE is intersecting them.

∠DEF = ∠DGC (Corresponding angles)

∠DEF = 70°

QUESTION 6

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

Sol :

(i)

Consider two lines, ** l** and

**, and a transversal line**

*m***which is intersecting them.**

*n*Sum of the interior angles on the same side of transversal = 126° + 44° = 170°

As the sum of interior angles on the same side of transversal is not 180°, therefore, ** l** is not parallel to

*m*

(ii)

** x** + 75° = 180° ( Linear pair on line

**)**

*l*** x** = 180°-75°

** x** = 105°

For ** l** and

**to be parallel to each other, corresponding angles (∠ABC and ∠x) should be equal.**

*m*However, here their measures are 75° and 105° respectively. Hence, these lines are not parallel to each other .

(iii)

∠x+123° = 180° (Linear pair)

∠x = 180° – 123°

∠x = 57°

For ** l** and

**to be parallel to each other, corresponding angles (∠ABC and ∠x) should be equal**

*m*Here, their measures are 57° and 57° respectively. Hence, these lines are parallel to each other.

(iv)

98° + ∠x = 180° (Linear pair)

∠x = 82°

For ** l** and

**to be parallel to each other, corresponding angles (∠ABC and ∠x) should be equal.**

*m*However, here their measures are 72° and 82° respectively. Hence, these lines are not parallel

to each other.