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Toggle**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 = 125^{0},∠c=55^{0}, ∠d = 125^{0}, ∠e = 55^{o} and ∠f = 55^{0}

**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 ≠ 72^{0} [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.