**NCERT Solutions for Class 7 Maths**

Chapter 5 Lines and Angles

Exercise 5.2

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.**

**(ii) If ∠4 = ∠6, then a || b.**

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

**Answer**

(i) Corresponding angles property is used in the above statement.

(ii) Alternate interior angles property is used in the above statement.

(iii) Interior angles on the same side of transversal are supplementary.

**2. 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.**

**Answer**

By observing the figure, the pairs of corresponding angle are,

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

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

∠2 and ∠8, ∠3 and ∠5

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

(iv) 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.**

**Answer**

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.**

Answer

(i) 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) By the property of corresponding angles,

∠x = 100^{o}

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

**If ∠ABC = 70º, then find**

**(i) ∠DGC**

**(ii) ∠DEF**

**Answer**

(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.**

**Answer**

(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 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) 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) Let us assume ∠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 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.

(iv) 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 72^{o} 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.