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

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

Ex 5.2 Class 7 Maths Question 1.

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

(i) If a || b, then âˆ 1 = âˆ 5

(ii) If âˆ 4 = âˆ 6, then a || b

(iii) If âˆ 4 + âˆ 5 = 180Â°, then a || b

Solution:

(i) Given a || b

âˆ´ âˆ 1 = âˆ 5 (Pair of corresponding angles)

(ii) Given: âˆ 4 = âˆ 6

âˆ´ a || b [If pair of alternate angles are equal, then the lines are parallel]

(iii) Given: âˆ 4 + âˆ 5 = 180Â°

âˆ´ a || b [If sum of interior angles is 180Â°, then the lines are parallel]

Ex 5.2 Class 7 MathsÂ Question 2.

In the given 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.

Solution:

(i) The pair of corresponding angles are âˆ 1 and âˆ 5, âˆ 2 and âˆ 6, âˆ 4 and âˆ 8, âˆ 3 and âˆ 7.

(ii) The pairs of alternate interior angles are âˆ 2 and âˆ 8, âˆ 3 and âˆ 5.

(iii) The pairs of interior angles on the same side of the transversal are âˆ 2 and âˆ 5, âˆ 3 and âˆ 8.

Ex 5.2 Class 7 MathsÂ Question 3.

In the given figure, p || q. Find the unknown angles.

Solution:

âˆ e + 125Â° = 180Â° (Linear pair)

âˆ´ âˆ e = 180Â° – 125Â° = 55Â°

âˆ e = âˆ f (Vertically opposite angles)

âˆ´ âˆ f= 55Â°

âˆ a = âˆ f= 55Â° (Alternate interior angles)

âˆ c = âˆ a = 55Â° (Vertically opposite angles)

âˆ d = 125Â° (Corresponding angles)

âˆ b = âˆ d = 125Â° (Vertically opposite angles)

Thus, âˆ a = 55Â°, âˆ b = 125Â°, âˆ c = 55Â°, âˆ d = 125Â°, âˆ e = 55Â°, âˆ f= 55Â°.

Ex 5.2 Class 7 MathsÂ Question 4.

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

Solution:

(i) Let the angle opposite to 110Â° be y.

âˆ´ y = 110Â° (Vertically opposite angles)

âˆ x + âˆ y = 180Â° (Sum of interior angle on the same side of transversal)

âˆ x + 110Â° = 180Â° .

âˆ´ âˆ x = 180Â° – 110Â° = 70Â°

Thus x= 70Â°

(ii) âˆ x = 110Â° (Pair of corresponding angles)

Ex 5.2 Class 7 MathsÂ Question 5.

In the given figure, the arms of two angles are parallel. If âˆ ABC = 70Â°, then find

(i) âˆ DGC

(ii) âˆ DEF

Solution:

Given

AB || DE

BC || EF

âˆ ABC = 70Â°

âˆ DGC = âˆ ABC

(i) âˆ DGC = 70Â° (Pair of corresponding angles)

âˆ DEF = âˆ DGC

(ii) âˆ DEF = 70Â° (Pair of corresponding angles)

Ex 5.2 Class 7 MathsÂ Question 6.

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

Solution:

Sum of interior angles on the same side of transversal

= 126Â° + 44Â° = 170Â° â‰ 180Â°

âˆ´ l is not parallel to m.

(ii) Let angle opposite to 75Â° be x.

x = 75Â° [Vertically opposite angles]

âˆ´ Sum of interior angles on the same side of transversal

= x + 75Â° = 75Â° + 75Â°

= 150Â° â‰ 180Â°

âˆ´ l is not parallel to m.

(iii) Let the angle opposite to 57Â° be y.

âˆ´ âˆ y = 57Â° (Vertically opposite angles)

âˆ´ Sum of interior angles on the same side of transversal

= 57Â° + 123Â° = 180Â°

âˆ´ l is parallel to m.

(iv) Let angle opposite to 72Â° be z.

âˆ´ z = 70Â° (Vertically opposite angle)

Sum of interior angles on the same side of transversal

= z + 98Â° = 72Â° + 98Â°

= 170Â° â‰ 180Â°

âˆ´ l is not parallel to m.

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