Haryana State Board HBSE 7th Class Maths Solutions Chapter 5 Lines and Angles InText Questions and Answers.

## Haryana Board 7th Class Maths Solutions Chapter 5 Lines and Angles InText Questions

Try These (Page No. 94):

Question 1.

List ten figures around you and identify the acute, obtuse and right angles found in them.

Solution:

Think, Discuss & Write (Page No. 95):

Question 1.

Can two acute angles be complement of each other ?

Solution:

Yes complementary 30° is and acute angle and 60° is also an acute angle.

30° + 60° = 90° (Complementary angle)

Question 2.

Can two obtuse angles be complement of each other ?

Solution:

No obtuse angle > 90°

Question 3.

Can two right angles be complement of each other ?

Solution:

No, one right angle = 90°

Try These (Page No. 95):

Question 1.

Which pairs of following angles are complementary ?

Solution:

(i) and (iv), because complementary angle = 90°.

Question 2.

What is the measure of the complement each of following given angles ?

(i) 45° (ii) 65° (iii) 41° (iv) 54°

Solution:

(i) Let the complement of 45° is re.

∴ x + 45° = 90°

or x = 90° -45° = 45°

∴ Complement of 45° is 45°.

(ii) Let the complement of 65° is x.

∴ x + 65° = 90°

or re = 90° -65° = 25°

∴ The complement of 65° is 25°.

(iii) Let the complement of 41° be m.

∴ m + 41° = 90°

or m = 90° – 41° = 49°

or m = 49°

Thus, the complement of 41° is 49°.

(iv) Let the complement of 54° be x.

∴ x + 54° = 90°

or re = 90° – 54° = 36°

Thus, the complement of 54° is 36°.

Question 1.

The difference in the measures of two complementary angles is 12°. Find the measures of the angles.

Solution:

90° -x = 12°

90° – 12° = x

or 78° = x

∴ x = 78°

Think, Discuss & Write (Page No. 96):

Question 1.

Can two obtuse angles be supplementary ?

Solution:

No, supplementary angle = 180°

obtuse > 90°.

Question 2.

Can two acute angles be supplementary ?

Solution:

Yes, acute angle < 90°

Question 3.

Can two right angles be supplementary ?

Solution:

Yes, right angle

= 90°

Try These (Page No. 97):

Question 1.

Find the supplementary angles in the following given pairs :

Solution:

(i) Measures of the given angles are 110° and 50°.

∵ 110°+ 50° = 160°.

and 160° ≠ 180°

∴ 110° and 50° are not a pair of supplementary angles.

(ii) Measures of the given angles are 105° and 65°.

∵ 105°+ 65° = 170°.

and 170° ≠ 180°

∴ 105° and 65° are not a pair of supplementary angles.

(iii) Measures of the given angles are 50° and 150°.

∵ 50° + 130° = 180°.

∴ 50° and 130° are a pair of supplementary angles.

(iv) Measures of the given angles are 45° and 45°.

∵ 45° + 45° = 90°. and 90° ≠ 180°

∴ 45° and 45° are not a pair of supplementary angles.

Question 1.

What will be the measure of the supplement of each one of the following angles ?

(i) 100° (ii) 90° (iii) 55° (iv) 125°

Solution:

(i) Let the supplementary of 100° be a.

∴ 100° + x = 180°

or x = 180° – 100° = 80°

∴ The measure of the supplement of 100° is 80°.

(ii) Let the supplementary of 90° be x.

∴ x + 90° = 180°

or x = 180°- 90° = 90°

The measure of the supplement of 90° is 90°.

(iii) Let the supplementary of 55° be x.

∴ 55° + x = 180°

or x = 180° -55° = 125°

The supplement of 55° is 125°.

(iv) Let the supplementary of 125° bey.

∴ y + 125° = 180°

or y = 180°-125° = 55°

∴ The supplement of 125° is 55°.

Question 2.

Among two supplementary angles the measure of the larger angle is 44° more than the measure of the smaller. Find their measures.

Solution:

A-t-q, x + x + 44 = 180°

or, 2x + 44 = 180°

2x = 180° – 44°

x = \(\frac{136}{2}\) = 68°

∴ 68°, 112°

Try These (Page No. 97-98):

Question 1.

Are the angles marked 1 and 2 adjacent ? If they are not adjacent.

Solution:

(i) Yes, (ii) Yes, (iii) No, (iv) Yes,

Yes.

(iii) No, because two angles in a plane are said to be adjacent angles, if they have a common vertex, a common arm and the other two arms on opposite sides of the common arm.

Question 2.

In the given figure are the following adjacent angles ?

(a) ∠AOB and ∠BOC

(b) ∠BOD and ∠BOC

Justify your answer.

Solution:

(a) Yes, because they have a common vertex O and a common arm OB.

(b) No, because they are not placed next to each other.

Think, Discuss & Write (Page No. 98):

Question 1.

Can two adjacent angles be supplementary ?

Solution:

Yes, because two adjacent angles form a supplementary.

Question 2.

Can two adjacent angles be complementary ?

Solution:

Y es, because two adjacent angles form a complementary.

Question 3.

Can two obtuse angles be adjacent angles ?

Solution:

Yes, in the figure, ∠BOC and ∠COD are obtuse angles and they are adjacent angles.

Question 4.

Can an acute angle be adjacent to an obtuse angle ?

Solution:

Yes, in the figure, ∠1 and ∠2 are adjacent angles. ∠1 is acute and ∠2 is an obtuse angle.

Think, Discuss & Write (Page No. 99):

Question 1.

Can two acute angles form a linear pair ?

Solution:

No, because acute angle < 90° and linear pair = 180°. Question 2. Can two obtuse angles form a linear pair ? Solution: No, because obtuse angle > 90°

and linear pair = 180°.

Question 2.

Can two right angles form a linear pair ?

Solution:

Yes, because right angle = 90°

and linear pair = 180°.

Try These (Page No. 99):

Question 1.

Check which of the following pairs of angles form a linear pair:

Solution:

(i) Yes,

∵ 140°+ 40° = 180°

∴ The given pair of angles form a linear pair.

(ii) No,

∵ 60° + 60° = 120°

and 120° ≠ 180°.

(iii) No,

∵ 90° + 80° = 170°

and 170° ≠ 180°.

(iv) Yes,

∵ 115°+ 65° = 180°.

Try These (Page No. 101):

Question 1.

In the given figure, if ∠1 = 30°. find ∠2 and ∠3.

Solution:

Since ∠1 + ∠2 = Linear pair = 180°

or, 30° + ∠2 = 180°

or, ∠2 = 180°-30°

∴ ∠2 = 150°

Now, ∠2 + ∠3 = 180°

or, 150° + ∠3 = 180°

or, ∠3 = 180° -150°

∴ ∠3 = 30°

or, ∠1 = ∠2 = vertically opposite angle

∴ 30° = ∠2

∴ ∠2 = 30°

Question 2.

Give an example for vertically opposite angles in your surroundings.

Solution:

Two angles formed by two intersecting lines having common arm are said to be vertically opposite angles.

Hence, ∠COB = ∠AOD = 60°

= vertically opposite angle

and ∠BOD = ∠AOC = 120°

= vertically opposite angles

Try These (Page No. 104):

Question 1.

Find examples from your surround-ings where lines intersect at right angles.

Solution:

(i) A black board, (ii) A table, (iii) A television (iv) A computer.

Question 2.

Find the measures of the angles made by the intersecting lines at the vertices of an equilateral triangle.

Solution:

Vertices, A, B and C. (Fig.)

Question 3.

Draw any rectangle and find the measures of angles at the four vertices made by the intersecting lines.

Solution:

Question 4.

If two lines intersect, do they always intersect at right angles ?

Solution:

Try These (Page No. 105):

Question 1.

Suppose Two lines are given. How many transversals can you draw for these lines.

Solution:

Many

Question 2.

If three lines have a transversal, how many points of intersections are there ?

Solution:

Three.

Question 3.

Try to identify a few transversals in your surroundings.

Solution:

Road, Rail, ladder etc.

Try These (Page No. 1.6):

Question 1.

Name the pairs of angles in each Figure.

Solution:

(ii) i.e. < 1 and < 2 are called pairs corresponding angles. [Fig. (i)]

(it) i.e. <3 and < 4 are called pairs of alternate interior angles. [Fig. (ii)]

(iii) i.e. < 5 and < 6 are called pairs of interior angles on the same side of the transversal. [Fig. (iii)]

(iv) i.e. < 7 and < 8 are called pairs of corresponding angles. [Fig.(iv)]

(v) i.e. < 9 and < 8 are called pairs of alternate interior angles. [Fig. (v)]

(vi) i.e. < 11 and < 12 are called linear pairs. [Fig. (vi)]

Try These (Page No. 109):

Question 1.

Solution:

(i) x = 60°

[∵ x and 60° are alternate interior angles]

(ii) ∠y = 55°

[∵ y and 55° are alternate interior angles]

(iii) If two non-parallel lines are intersected by a transversal, then the angle of pairs of alternate interior angles are not equal.

Hence ∠1 = ∠2

(iv) 60° + z = 180°

⇒ z = 180° – 60°

z = 120°

x = 120°

[ ∵ and 60° are interior angles on the same side of the transversal]

∴ z = 120°.

(v) x = 120°

[∵ x and 120° are corresponding angles]

(vi) a + 60° = 180°

⇒ a = 180° – 60° = 120°

a – c

⇒ c = 120° [alternate angles]

c = b

[vertically opp. angles]

⇒ b = 120° [linear pair]

⇒ b+d = 180°

⇒ 120° + d = 180°

∴ d = 180° – 120° = 60°.

Try These (Page No. 100):

Question 1.

Solution:

(i) Yes, l || m, because alternate interior angles are equal and 50°.

(ii) Yes, l || m, because alternate interior angles are equal and 50°.

(iii) If two parallel lines are intersected by a transversal, then the sum of the interior angles on the same side of the transversal is 180° or supplementary.

Hence, 180° + x = 180°

or, x = 180° -180°

x = 0°

But in this figure one angle is 180°. Hence it is not possible.