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You are here: Home / NCERT Solutions / Class 7 / Maths / NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Exercise 5.2

NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Exercise 5.2

Last Updated on February 16, 2022 By Mrs Shilpi Nagpal Leave a Comment

NCERT Solutions for Class 7 Maths
Chapter 5 Lines and Angles
Exercise 5.2

  • Class 7 Maths Lines and Angles Exercise 5.1
  • Class 7 Maths 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.

Class 7 Maths Chapter 5 Lines and Angles Exercise 5.2

Answer

(i) We have, if $a \| b$, then $\angle 1=\angle 5$.
If a transversal intersects two parallel lines, then the corresponding angles are equal.
$\therefore$ By corresponding angle property, it is true.

(ii) We have, if $\angle 4=\angle 6$, then $a \| b$.
If a transversal intersects two parallel lines, then the alternate interior angles are equal.
$\therefore$ By alternate interior angle property, it is true.(iii) We have, if $\angle 4+\angle 5=180^{\circ}$, then $a \| b$.
If a transversal intersects two parallel lines, then the interior angles on the same side of the 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.

Class 7 Maths Chapter 5 Lines and Angles Exercise 5.2

Answer

(i) Pairs of corresponding angles are
$\angle 1, \angle 5 ; \angle 2, \angle 6 ; \angle 3, \angle 7 ; \angle 4, \angle 8$

(ii) Pairs of alternate interior angles are $\angle 2, \angle 8 ; \angle 3, \angle 5$.

(iii) Pairs of interior angles on the same sides of the transversal are
$\angle 2, \angle 5 ; \angle 3, \angle 8$.

(iv) Vertically opposite angles are
$\angle 1, \angle 3 ; \angle 2, \angle 4 ; \angle 5, \angle 7 ; \angle 6, \angle 8$.

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

Class 7 Maths Chapter 5 Lines and Angles Exercise 5.2

Answer

Given, $p \| q$

∠e + 125° = 180°   (by linear pair)

⇒ ∠e = 180° – 125 ⇒ ∠e = 55°

∴ ∠f = ∠e = 55°   (vertically opposite angles)

Since, $p \| q$ and t is a transversal.

∴ ∠a = ∠f = 55° (alternate interior angles)

∠d = 125° (corresponding angles)

∠c = ∠a  = 55° (vertically opposite angles)

and  ∠b = ∠d = 125°  (vertically opposite angle)

Hence, ∠a = 55°, ∠b = 125°, ∠c = 55°, ∠d = 125° and ∠f = 55°.

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

Class 7 Maths Chapter 5 Lines and Angles Exercise 5.2
Answer

(i) We have, $l \| m$ and $t$ is a transversal. (alternate interior angles)

$\therefore \quad \angle x=\angle 1$

Now, $\angle 1+110^{\circ}=180^{\circ} \quad$ [by linear pair]

$\therefore \quad \angle 1=180^{\circ}-110^{\circ}=70^{\circ}$

$\therefore \quad \angle x=70^{\circ}$

Hence, the required value of $x$ is $70^{\circ}$.

(ii) Since, $l \| m$ and $a$ is a transversal.

Hence, the required value of x is 100°.

5. In the given figure, the arms of two angles are parallel.
If ∠ABC = 70º, then find
(i) ∠DGC
(ii) ∠DEF

Class 7 Maths Chapter 5 Lines and Angles Exercise 5.2

Answer

(i) Given, ∠ABC = 70°
Since, $AB \| DE$ and BC is a transversal.
∴ ∠DGC = ∠ABC = 70° (corresponding angles)
Hence, the value of  ∠DGC is 70°

(ii) Since, $BC \| EF$ and DE is a transversal.
∴ ∠DEF = ∠DGC = 70° (corresponding angles)
Hence, the value of  ∠DEF is 70°

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

Class 7 Maths Chapter 5 Lines and Angles Exercise 5.2

Answer

(i) Since, $44^{\circ}+126^{\circ}=170^{\circ}$
But $\quad 170^{\circ} \neq 180^{\circ}$
i.e. the sum of the interior angles on the same side of the transversal is not $180^{\circ} .$
So, $l$ and $m$ are not parallel.

(ii) Since, $n$ is a transversal to $l$ and $m .$
$\therefore \quad \angle 1=75^{\circ}$ (vertically opposite angles)
Also, $\quad \angle 1=75^{\circ}=75^{\circ}+75^{\circ}=150^{\circ}$
$\therefore \quad 150^{\circ} \neq 180^{\circ}$
So, $l$ and $m$ are not parallel.

(iii) Since, $\angle 1+123^{\circ}=180^{\circ}$ (by linear pair)
$\Rightarrow \angle 1=180^{\circ}-123^{\circ} \Rightarrow \angle 1=57^{\circ}$

So, $l$ and $m$ are parallel.

(iv) Since, $\angle 1+98^{\circ}=180^{\circ} \quad$ (by linear pair)
$\therefore $ $\angle 1=180^{\circ}-98^{\circ}=82^{\circ}$
Let  $\angle 2=98^{\circ}$ and $\angle 3=72^{\circ}$
$\therefore $ $\angle 1 \neq \angle 3$
i.e., the corresponding angles are not equal.
So, l and m are not parallel.

Filed Under: Class 7, Maths, NCERT Solutions

About Mrs Shilpi Nagpal

Author of this website, Mrs Shilpi Nagpal is MSc (Hons, Chemistry) and BSc (Hons, Chemistry) from Delhi University, B.Ed (I. P. University) and has many years of experience in teaching. She has started this educational website with the mindset of spreading Free Education to everyone.

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