SCERT AP 7th Class Maths Solutions Pdf Chapter 4 Lines and Angles Ex 4.1 Textbook Exercise Questions and Answers.

## AP State Syllabus 7th Class Maths Solutions 4th Lesson Lines and Angles Exercise 4.1

Question 1.

Find which of the following pair of angles are complementary and which are supplementary?

Answer:

90° + 20° = 1 10° ≠ 90° (or) ≠ 180°

So, they are not complementary or not supplementary.

Answer:

6o° + 30° = 90°

So, they are complementary angles.

Answer:

11°+ 79° = 90°

So, they arc complementary angles.

Answer:

125° + 55° = 180°

So, they are supplementary angles.

Answer:

50 + 130° = 180°

So, they are supplementary angles.

Answer:

40° + 120° = 160° ≠ 90° (or) 180°

So, they are not complementary angles or not supplementary angles.

Question 2.

If the ratio of two complementary angles is 2:3, then find the two angles.

Answer:

Given the ratio of two complementary angles = 2 : 3 = 2x : 3x

Sum of the complementary angles = 90° So, 2x + 3x = 90°

⇒ 5x = 90°

⇒ \(\frac{5 x}{5}=\frac{90^{\circ}}{5}\)

∴ x = 18°

Then the angles are

2x, 3x = 2(18°), 3(18°) = 36°, 54°

Question 3.

In the figure, ∠A and ∠Q are complementary angles. Find the value of x.

Answer:

Given ∠A = 9x°, ∠Q = 36° and

∠A and ∠Q are complementary angles.

So, ∠A + ∠Q = 90°

⇒ 9x + 36° = 90°

⇒ 9x + 36° – 36° = 90° – 36°

⇒ 9x = 54°

⇒ \(\frac{9 \mathrm{x}}{9}=\frac{54^{\circ}}{9}\)

⇒ x = 6° .

Question 4.

If ∠A and ∠B are conjugate angles and ∠A = ∠B. Find the two angles.

Answer:

Given ∠A and ∠B are conjugate angles and

∠A = ∠B = x°

So, ∠A + ∠B = 360°

⇒ x° + x° – 360°

⇒ 2x° = 360°

⇒ \(\frac{2 x}{2}=\frac{360^{\circ}}{2}\)

⇒ x = 180°

∴ ∠A = ∠B = x° = 180°

Question 5.

Draw a pair of complementary angles and a pair of supplementary angles.

Answer:

Question 6.

Teacher asked students to draw the complementary angle to the given angle. The students have drawn as follows. Who is correct?

Answer:

Sum of the two angles is 90°, then they are called complementary angles.

Complementary angle of 30° is 60°. So, Sujatha is correct.

Question 7.

In the given figure, ∠B and ∠E are supplementary angles. Find x.

Answer:

Given ∠B and ∠E are supplementary angles.

∠B + ∠E = 180°

⇒ 30° + 5x = 180°

⇒ 30° + 5x – 30° = 180°- 30°

⇒ 5x = 150°

⇒ \(\frac{5 x}{5}=\frac{150^{\circ}}{5}\)

∴ x = 30°

Question 8.

Ashritha said, “In the pair of supplementary angles, one angle must be obtuse angle.” Do you agree? Give reason.

Answer:

No, two acute angles cannot make supplementary angles. Two right angles (90°) can make supplementary angles. One acute and one obtuse angles can make supplementary angles.

Question 9.

Find the angle which is 40° more than its supplementary angle?

Answer:

Let one angle is x°.

Other angle is (x + 40)°.

Given two angles are supplementary.

So, x + x + 40° = 180°

⇒ 2x + 40° = 180°

⇒ 2x + 40° – 40° = 180° – 40°

⇒ 2x = 140°

⇒ \(\frac{2 x}{2}=\frac{140^{\circ}}{2}\)

Angle x = 70°

Other angle is x + 40° = 70° + 40° = 110°

∴ Angles are 70° and 110°.

Question 10.

Srinu said, “Two obtuse angles cannot be supplementary.” Do you agree? Justify your answer.

Answer:

Yes, sum of two obtuse angles is greater than 180°.