NCERT Solution For Class Class 7, Maths, Lines And Angles, Exercise 5.2

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NCERT Solution For Class Class 7, Maths, Lines And Angles, Exercise 5.2 has total six question to practice. Class 7 maths chapter 5 exercise 5.1 is given below. Ex 5.2 class 7 is basically about acute, obtuse and Right angle figure in which students need to find required angles by using suitable method.

NCERT Solution For Class Class 7, Maths, Lines And Angles, Exercise 5.2

Q.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.

Ans:

(i) If a || b, then ∠1 = ∠5.

Corresponding angles

(ii) If ∠4 = ∠6, then a || b.

Alternate interior angles

(iii) If ∠4 + ∠5 = 180°, then a || b.

Interior angles

Q.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.

Ans: (i) the pairs of corresponding angles.

The pairs of corresponding angles are, ∠1 and ∠5, ∠4 and ∠8, ∠2 and ∠6, ∠3 and ∠7.

(ii) the pairs of alternate interior angles.

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.

The pairs of interior angles on the same side of the transversal are ∠2 and ∠5, ∠3 and ∠8.

(iv) the vertically opposite angles.

The vertically opposite angles are, ∠1 and ∠3, ∠5 and ∠7, ∠2 and ∠4, ∠6 and ∠8.

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

Ans: ∠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

Now, ∠e = ∠f = 55^o [vertically opposite angles]

∠b = ∠d = 125^o

Also, ∠c = ∠f = 55^o [Corresponding angles]

∠a = ∠e = 55^o

Thus, ∠a = 55^o , ∠b = 125⁰,∠c=55⁰, ∠d = 125⁰, ∠e = 55^o and ∠f = 55⁰

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

Ans: (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

Q.5. In the given figure, the arms of two angles are parallel. If ∠ABC = 70º, then find

(i) ∠DGC

(ii) ∠DEF

Ans: (i) Given, AB || DG and BC is the transversal line intersecting AB and DG

∠DGC = ∠ABC [Corresponding angles]

Then,

∠DGC = 70^o

(ii) Given that BC|| EF and DE is the transversal line intersecting BC and EF

∠DEF = ∠DGC [Corresponding angles]

Then,

∠DEF = 70^o

Q.6. In the given figures below, decide whether l is parallel to m.

Ans: (i) Let us consider the two lines l and m, n is the transversal line intersecting l and m.

∵ 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 ∠x be the vertically opposite angle formed due to the intersection of the straight line l and transversal n,

Then, ∠x = 75^o

Now, we have 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 ∠x be the vertically opposite angle formed due to the intersection of the Straight-line l and transversal line n,

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,

∵ 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, ∠x ≠ 72⁰ [Corresponding angles]

For l and m to be parallel to each other, corresponding angles should be equal. So, Line l is not parallel to line m.

Chapter 5, Lines and Angles

Class 7, Maths, Lines and Angles, Exercise 5.1
Class 7, Maths, Lines and Angles, Exercise 5.2