Tuesday, May 26, 2020

NCERT solution class 7 chapter 5 exercise 5.2 mathematics

Exercise 5.2



Introduction - Ex 5.2 "Lines and Angles" Chapter 5 - NCERT Class 7th Maths


Q 1, Ex 5.2 - Lines and Angles - Chapter 5 - Maths Class 7th - NCERT


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

(i) If a || b, then ∠1 = ∠5
Sol :  Corresponding angles property

(ii) If ∠4 = ∠6 , then a || b
Sol :  Alternate interior angles property

(iii) If ∠4 + ∠5 = 180° , then a || b
Sol :  Interior angles on the same side of transversal are supplementary.


Q 2, Ex 5.2 - Lines and Angles - Chapter 5 - Maths Class 7th - NCERT



QUESTION 2
In the adjoining figure, identify

(i) The pairs of corresponding angles
Sol :
∠1 and ∠5 , ∠2 and ∠6 , ∠3 and ∠7 , ∠4 and ∠8

(ii) The pairs of alternate interior angles
Sol :
∠2 and ∠8 , ∠3 and ∠5

(iii) The pairs of interior angles on the same side of the transversal
Sol :
∠2 and ∠5 , ∠3 and ∠8

(iv) The vertically opposite angles
Sol :
∠1 and ∠3 , ∠2 and ∠4 , ∠5 and ∠7 , ∠6 and ∠8


Q 3, Ex 5.2 - Lines and Angles - Chapter 5 - Maths Class 7th - NCERT



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

Sol :
∠d = 125° (Corresponding angles)
∠e = 180° - 125° = 55° (Linear pair)
∠f= ∠e = 55° (Vertically opposite angles)
∠c = f = 55° (Corresponding angles)
∠a = ∠e = 55° (Corresponding angles)
∠b = ∠d = 125° (Vertically opposite angles)


Q 4, Ex 5.2 - Lines and Angles - Chapter 5 - Maths Class 7th - NCERT



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

Sol :
(i)

∠y = 110° (Corresponding angles)
∠x + ∠y = 180° (Linear pair)
∠y = 180° - 110°
∠y = 70°

(ii)

∠x = 100° (Corresponding angles)


Q 5, Ex 5.2 - Lines and Angles - Chapter 5 - Maths Class 7th - NCERT



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

If ∠ABC = 70°, then find
(i) ∠DGC
Sol :
(i) Consider that AB || DG and a transversal line BC is intersecting them.
∠DGC = ∠ABC (Corresponding angles)
∠DGC = 70°

(ii) ∠DEF
Sol :
(ii) Consider that BC || EF and a transversal line DE is intersecting them.
∠DEF = ∠DGC (Corresponding angles)
∠DEF = 70°


Q 6, Ex 5.2 - Lines and Angles - Chapter 5 - Maths Class 7th - NCERT



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

Sol :
(i)

Consider two lines, l and m , and a transversal line n which is intersecting them.
Sum of the interior angles on the same side of transversal = 126° + 44° = 170°
As the sum of interior angles on the same side of transversal is not 180°, therefore, l is not parallel to m

(ii)

x + 75° = 180° ( Linear pair on line )
x = 180°-75°
x = 105°
For l and m to be parallel to each other, corresponding angles (∠ABC and ∠x) should be equal.
However, here their measures are 75° and 105° respectively. Hence, these lines are not parallel to each other .

(iii)

∠x+123° = 180° (Linear pair)
∠x = 180° - 123°
∠x =  57°
For l and m to be parallel to each other, corresponding angles (∠ABC and ∠x) should be equal
Here, their measures are 57° and 57° respectively. Hence, these lines are parallel to each other.

(iv)

98° + ∠x = 180° (Linear pair)
∠x = 82°
For l and m to be parallel to each other, corresponding angles (∠ABC and ∠x) should be equal.
However, here their measures are 72° and 82° respectively. Hence, these lines are not parallel
to each other.

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