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

NCERT Solutions for Class 7 Maths Exercise 5.2 Chapter 5 Lines and Angles in simple PDF are given here. The exercise of NCERT Solutions for Class 7 Maths Chapter 5 has topics related to pairs of lines such as, intersecting lines, transversal and angles made by a transversal, transversal of parallel lines, checking of parallel lines. A line that intersects two or more lines at distinct points is a transversal line. Two lines intersect if they have a point in common. Students are suggested to try solving the questions from NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles and then refer to these solutions to identify the most competent way of approaching different problems.

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### Access answers to Maths NCERT Solutions for Class 7 Chapter 5 â€“ Lines and Angles Exercise 5.2

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

(i) If a âˆ¥ b, then âˆ 1 = âˆ 5.

Solution:-

Corresponding angles property is used in the above statement.

(ii) If âˆ 4 = âˆ 6, then a âˆ¥ b.

Solution:-

Alternate interior angles property is used in the above statement.

(iii) If âˆ 4 + âˆ 5 = 180o, then a âˆ¥ b.

Solution:-

Interior angles on the same side of transversal are supplementary.

2. In the adjoining figure, identify

(i) The pairs of corresponding angles.

Solution:-

By observing the figure, the pairs of corresponding angle are,

âˆ 1 and âˆ 5, âˆ 4 and âˆ 8, âˆ 2 and âˆ 6, âˆ 3 and âˆ 7

(ii) The pairs of alternate interior angles.

Solution:-

By observing the figure, the pairs of alternate interior angle are,

âˆ 2 and âˆ 8, âˆ 3 and âˆ 5

(iii) The pairs of interior angles on the same side of the transversal.

Solution:-

By observing the figure, the pairs of interior angles on the same side of the transversal are âˆ 2 and âˆ 5, âˆ 3 and âˆ 8

(iv) The vertically opposite angles.

Solution:-

By observing the figure, the vertically opposite angles are,

âˆ 1 and âˆ 3, âˆ 5 and âˆ 7, âˆ 2 and âˆ 4, âˆ 6 and âˆ 8

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

Solution:-

By observing the figure,

âˆ d = âˆ 125o â€¦ [âˆµ corresponding angles]

We know that, Linear pair is the sum of adjacent angles is 180o

Then,

= âˆ e + 125o = 180o â€¦ [Linear pair]

= âˆ e = 180o â€“ 125o

= âˆ e = 55o

From the rule of vertically opposite angles,

âˆ f = âˆ e = 55o

âˆ b = âˆ d = 125o

By the property of corresponding angles,

âˆ c = âˆ f = 55o

âˆ a = âˆ e = 55o

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

(i)

Solution:-

Let us assume other angle on the line m be âˆ y,

Then,

By the property of corresponding angles,

âˆ y = 110o

We know that Linear pair is the sum of adjacent angles is 180o

Then,

= âˆ x + âˆ y = 180o

= âˆ x + 110o = 180o

= âˆ x = 180o â€“ 110o

= âˆ x = 70o

(ii)

Solution:-

By the property of corresponding angles,

âˆ x = 100o

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

If âˆ ABC = 70o, then find

(i) âˆ DGC

(ii) âˆ DEF

Solution:-

(i) Let us consider that AB âˆ¥ DG

BC is the transversal line intersecting AB and DG

By the property of corresponding angles,

âˆ DGC = âˆ ABC

Then,

âˆ DGC = 70o

(ii) Let us consider that BC âˆ¥ EF

DE is the transversal line intersecting BC and EF

By the property of corresponding angles,

âˆ DEF = âˆ DGC

Then,

âˆ DEF = 70o

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

(i)

Solution:-

Let us consider the 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 180o.

Then,

= 126o + 44o

= 170o

But, the sum of interior angles on the same side of transversal is not equal to 180o.

So, line l is not parallel to line m.

(ii)

Solution:-

Let us assume âˆ x be the vertically opposite angle formed due to the intersection of the straight line l and transversal n,

Then, âˆ x = 75o

Let us consider the 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 180o.

Then,

= 75o + 75o

= 150o

But, the sum of interior angles on the same side of transversal is not equal to 180o.

So, line l is not parallel to line m.

(iii)

Solution:-

Let us assume âˆ x be the vertically opposite angle formed due to the intersection of the Straight line l and transversal line n,

Let us consider the 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 180o.

Then,

= 123o + âˆ x

= 123o + 57o

= 180o

âˆ´The sum of interior angles on the same side of transversal is equal to 180o.

So, line l is parallel to line m.

(iv)

Solution:-

Let us assume âˆ x be the angle formed due to the intersection of the Straight line l and transversal line n,

We know that Linear pair is the sum of adjacent angles is equal to 180o.

= âˆ x + 98o = 180o

= âˆ x = 180o â€“ 98o

= âˆ x = 82o

Now, we consider âˆ x and 72o are the corresponding angles.

For l and m to be parallel to each other, corresponding angles should be equal.

But, in the given figure corresponding angles measures 82o and 72o respectively.

âˆ´Line l is not parallel to line m.

### Access other exercises of NCERT Solutions For Class 7 Chapter 5 â€“ Lines and Angles

Exercise 5.1 Solutions