Well-designed AP 7th Class Maths Guide Chapter 5 Lines and Angles InText Questions offers step-by-step explanations to help students understand problem-solving strategies.

## AP 7th Class Maths 5th Chapter Data Handling InText Questions

Try These (Page No. 150)

Question 1.

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

Solution:

Class room activity.

Think discuss and write (Page No: 152)

Question 1.

Can two acute angles be complement to each other?

Solution:

Yes, two acute angles can be complementary. Acute angles are angles less than 90°.

Ex: 30° and 60° angles. Their sum is 90°, so, they complement each other.

Question 2.

Can two obtuse angles be complement to each other?

Solution:

Angles measuring than 90° are called obtuse angles. Ex : ∠100° and ∠120° are obtuse angle and their sum is 220°. Thus, they are not complement to each other.

Question 3.

Can two right angles be complement to each other?

Solution:

Two right angles cannot be complement to each other.

Try These (Page No. 152)

Question 1.

Which pairs of following angles are complementary? (Fig.)

i)

Solution:

70° + 20° = 90°

∴ The angles are complementary.

ii)

Solution:

75° + 25° = 100° > 90°

∴ The angles are not complementary.

iii)

Solution:

48° + 52° = 100° > 90°

∴ The angles are not complementary.

iv)

Solution:

35° + 55° = 90°

∴ The angles are complementary.

Question 2.

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

i) 45°

Solution:

Complement of 45° = 90° – 45° = 45°

ii) 65°

Solution:

Complement of 65° = 90° – 65° = 25°

iii) 41°

Solution:

Complement of 41° = 90° – 41° = 49°

iv) 54°

Solution:

Complement of 54° = 90° – 54° = 36°

Question 3.

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

Solution:

Method 1 :

x + y = 90°

\(\frac{x-y=12^{\circ}}{2 x=102}\)

x = \(\frac{102^{\circ}}{2}\) = 51°

y = 90° – 51° = 39°

∴ 51° and 39° on the two complementary angles.

(OR)

Method 2:

Let the first angle = x

Second angle = 90 – x

According to the problem

x – (90 – x) = 12

x – 90 + x = 12

2x = 12 + 90

2x = 102

x = \(\frac { 102 }{ 2 }\) ⇒ x = 51

90 – x = 90 – 51° = 39°

∴ The angle are 51° and 39°

Think discuss and write (Page No. 154)

Question 1.

Can two obtuse angles be supplementary?

Solution:

No, sum will exceed 180°

Question 2.

Can two acute angles be supplementary?

Solution:

No, sum will be less than 180°

Question 3.

Can two right angles be supplementary?

Solution:

Yes, sum will be 180°

Try These (Page No. 154)

Question 1.

Find the pairs of supplementary angles in Fig.

i)

Solution:

110° + 50° = 160°

Not Supplementary angles

ii)

Solution:

105° + 65° = 170°

Not Supplementary angles

iii)

Solution:

50° + 130° = 180°

Supplementary angles

iv)

Solution:

45° + 45° = 90°

Not Supplementary angles

Question 2.

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

i) 100°

Solution:

The measure of supplementary angle of 100° = 180° – 100° = 80°

ii) 90°

Solution:

The measure of supplementary angle of 90° = 180° – 90° = 90°

iii) 55°

Solution:

The measure of supplementary angle of 55° = 180° – 55° = 125°

iv) 125°

Solution:

The measure of supplementary angle of 125° = 180° – 125° = 55°

Question 3.

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

Solution:

Let the smaller angle = x°

Larger angle = x° + 44°

According to the problem

The angles are supplementary

∴ x° + x° + 44° = 180°

2x° + 180° – 44°

2x° = 136°

x° = \(\frac{136^{\circ}}{2}\)

x° = 68°

x° + 44° = 68° + 44° = 112°

∴ The angles are 68° and 112°

Think, discuss and write (Page No. 158)

Question 1.

In Fig. AC and BE intersect at P.

AC and BC intersect at C, AC and EC intersect at C.

Try to find another ten pairs of intersecting line segments.

Should any two lines or line segments necessarily intersect ? Can you find two pairs of non-intersecting line segments in the figure?

Can two lines intersect in more than one point? Think about it.

Solution:

Pairs of intersecting line segments.

BC and BE – B

BC and AC – C

AC and EC – C

AC and BE – P

BC and CE – C

BE and CE – E

Total 6 pairs are intersecting.

Yes, any two lines are intersecting in this figure.

Any two lines are necessarily intersecting only when they are not parallel.

No, two lines cannot intersect at two or more points.

This is possible only when both lines coincide. These lines intersect at infinite number of points

Try These (Page No. 160)

Question 1.

Find examples from your surroundings where lines intersect at right angles.

Solution:

Class room activity.

Ex : Edge of paper sheet.

Question 2.

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

Solution:

Each angle will be equal to other

∴ Measure of each angle = \(\frac{180^{\circ}}{3}\) = 60°

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:

No, it need not be that they intersect at right angles.

Try These (Page No. 162)

Question 1.

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

Solution:

Infinite.

Question 2.

If a line is a transversal to three lines, how many points of intersections are there?

Solution:

Question 3.

Try to identify a few transversals in your surroundings.

Solution:

Class room activity.

Ex: Mesh in Tennis bat.

Try These (Page No. 164)

Question 1.

Name the pairs of angles in each figure:

Solution:

- ∠1 and ∠2 are corresponding angles.
- ∠3 and ∠4 are alternate interior angles.
- ∠5 and∠6 are interior angles on the same side of transversal.
- ∠7 and∠8 are corresponding angles.
- ∠9 and ∠10 are alternate interior angles.
- ∠11 and ∠12 are linear pair of angles.

Do This (Page No. 164)

Question 1.

Take a ruled sheet of paper. Draw (in thick colour) two parallel lines I and m. Draw a transversal l to the lines l and m . Label ∠1 and ∠2 as shown fig. (i). Place a tracing paper over the figure drawn. Trace the lines l, m and t. Slide the tracing paper along t, until l coincides with m .

You find that ∠1 on the traced figure coincides with ∠2 of the original figure.

In fact, you can see all the following results by similar tracing and sliding activity.

i) ∠1 = ∠2

ii) ∠3 = ∠4

iii) ∠5 = ∠6

iv) ∠7 = ∠8

Solution:

Student Activity.

Do This (Page No. 168)

Question 1.

Draw a pair of parallel lines and a transversal. Verify the above three statements by actually measuring the angles.

Solution:

Students self activity.

Try these (Page No. 170)

Question 1.

i)

Lines l // m; t is a transversal ∠x = ?

Solution:

l // m

t is the tranversal

∠x = 60°

If a transversal intersects two parallel lines, then alternate interior angles are equal.

ii)

Lines a //b; c is a transversal ∠y =?

Solution:

a//b

c is a transversal

If a transversal intersects two parallel lines, then alternate interior angles are equal.

iii)

l_{1}, l_{2} be two lines t is a transversal. Is ∠1 = ∠2?

Solution:

l_{1}, l_{2} be two lines

t is a transversal

l_{1} & l_{2} are not parallel lines

∴ ∠1 ≠ ∠2

iv)

Lines l //m; t is a transversal ∠z= ?

Solution:

l//m

t is a transversal

If a transversal intersects two parallel lines, then sum of interior angles in the same side of the transversal is supplementary.

v)

Lines l//m; t is a transversal ∠x =?

Solution:

l//m

t is a transversal

If a transversal intersects two parallel lines, then corresponding angles are equal

x° = 120°

vi)

Lines l//m, p//q, Find a, b, c, d

Solution:

l // m

p || q

l //m, then p & q are transversals

p // m and l is the transversal

a + 60° = 180° (Sum of interior angles on the same side of transversal)

a = 180° – 60°

a = 120°

l // m, and q is the transversal.

∠a = ∠c = 120° (Alternate interior angles)

∴ ∠c = 120°

∠b = ∠c = 120°(Vertically opposite angles)

∴ ∠b = 120°

∠c + ∠d = 180° (Linear pair)

120 + ∠d = 180°

∠d = 180° – 120°

∠d = 60°

Try these (Page No. 172)

Question 1.

i)

Is l || m? Why?

Solution:

50° = 50°

l and m are two lines

t is the transversal

Then alternate interior angles are equal

∴ l || m

ii)

Is l || m? Why?

Solution:

Let us take the figure is the following way l and m are two lines

t is the transversal let x = 50° (Alternate angles)

x° + 130° = 50° + 130° = 180°

∴ l || m

iii)

Is l || m, what is ∠x?

Solution:

l || m

t is a transversal

70° + x° = 180°

(Interior angles on the same side of the transversal are supplementary)

x° = 180° – 70°

x° = 110°