NCERT Solutions Class 7th Math Chapter – 5 Lines and Angles Exercise – 5.2

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

(i) If a ∥ b, then ∠1 = ∠5.
Solution:  Corresponding angles property is used in the above statement.

(ii) If ∠4 = ∠6, then a ∥ b.
Solution: Alternate interior angles property is used in the above statement.

(iii) If ∠4 + ∠5 = 180^o, then a ∥ b.
Solution: Interior angles on the same side of transversal are supplementary.

2. In the adjoining figure, identify

(i) The pairs of corresponding angles.
Solution: By observing the figure, the pairs of corresponding angle are,∠1 and ∠5, ∠4 and ∠8, ∠2 and ∠6, ∠3 and ∠7

(ii) The pairs of alternate interior angles.
Solution:  By observing the figure, the pairs of alternate interior angle are,∠2 and ∠8, ∠3 and ∠5

(iii) The pairs of interior angles on the same side of the transversal.
Solution:  By observing the figure, the pairs of interior angles on the same side of the transversal are ∠2 and ∠5, ∠3 and ∠8

(iv) The vertically opposite angles.
Solution:  By observing the figure, the vertically opposite angles are,∠1 and ∠3, ∠5 and ∠7, ∠2 and ∠4, ∠6 and ∠8

3. In the adjoining figure, p ∥ q. Find the unknown angles.

Solution: By observing the figure,
∠d = ∠125^o … [∵ corresponding angles]
We know that, Linear pair is the sum of adjacent angles is 180^o
Then,
= ∠e + 125^o = 180^o … [Linear pair]
= ∠e = 180^o – 125^o
= ∠e = 55^o
From the rule of vertically opposite angles,
∠f = ∠e = 55^o
∠b = ∠d = 125^o
By the property of corresponding angles,
∠c = ∠f = 55^o
∠a = ∠e = 55^o

4. Find the value of x in each of the following figures if l ∥ m.

(i)

Solution: Let us assume other angle on the line m be ∠y,

Then,
By the property of corresponding angles,
∠y = 110^o
We know that Linear pair is the sum of adjacent angles is 180^o
Then,
= ∠x + ∠y = 180^o
= ∠x + 110^o = 180^o
= ∠x = 180^o – 110^o
= ∠x = 70^o

(ii)

Solution: By the property of corresponding angles,
∠x = 100^o

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

If ∠ABC = 70^o, then find
(i) ∠DGC
(ii) ∠DEF

Solution: 
(i) Let us consider that AB ∥ DG
BC is the transversal line intersecting AB and DG
By the property of corresponding angles,
∠DGC = ∠ABC
Then,
∠DGC = 70^o

(ii) Let us consider that BC ∥ EF
DE is the transversal line intersecting BC and EF
By the property of corresponding angles,
∠DEF = ∠DGC
Then,
∠DEF = 70^o

6. In the given figures below, decide whether l is parallel to m.
(i)

Solution: 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 transversal is 180^o.
Then,
= 126^o + 44^o
= 170^o

But, the sum of interior angles on the same side of transversal is not equal to 180^o.
So, line l is not parallel to line m.

(ii)

Solution: Let us assume ∠x be the vertically opposite angle formed due to the intersection of the straight line l and transversal n,
Then, ∠x = 75^o

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 transversal is 180^o.
Then,
= 75^o + 75^o
= 150^o

But, the sum of interior angles on the same side of transversal is not equal to 180^o.
So, line l is not parallel to line m.

(iii)

Solution: Let us assume ∠x be the vertically opposite angle formed due to the intersection of the Straight line l and transversal line m.

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 transversal is 180^o.
Then,
= 123^o + ∠x
= 123^o + 57^o
= 180^o

∴ The sum of interior angles on the same side of transversal is equal to 180^o.
So, line l is parallel to line m.

(vi)

Solution: Let us assume ∠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 180^o.
= ∠x + 98^o = 180^o
= ∠x = 180^o – 98^o
= ∠x = 82^o

Now, we consider ∠x and 72o 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 82^o and 72^o respectively.

∴ Line l is not parallel to line m.