# 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

(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 m , and a transversal line n which is intersecting them.

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 )

x = 180°-75°

x = 105°

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

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

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 m to be parallel to each other, corresponding angles (∠ABC and ∠x) should be equal.
However, here their measures are 72° and 82° respectively. Hence, these lines are not parallel
to each other.