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

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

Question 1.

Find the complementary, supplementary, and conjugate angle of 36°.

Answer:

Complementary angle of 36° is 90° – 36° – 54°

Supplementary angle of 36° is 180° – 36° = 144°

Conjugate angle of 36° is 360° – 36° = 324°

Question 2.

Observe the figure and write any 4 pairs of adjacent angles.

Answer:

Adjacent angle of ∠AOB is ∠BOC.

Adjacent angle of ∠BOC is ∠COD.

Adjacent angle of ∠COD is ∠DOE.

Adjacent angle of ∠DOE is ∠EOF.

Question 3.

In the given figure the lines l and m intersect at O. Find x.

Answer:

Given l and m intersecting at O.

x° + 40° = 120° (vertically opposite angles)

x + 40° – 40°= 120° – 40°

∴ x = 80°

Question 4.

In the given figure \(\overline{\mathbf{A E}}\) is a straight line. If the ratio of angles ∠1, ∠2, ∠3, ∠4 in the given figure is 1:2 :3 : 4, then find the angles.

Answer:

Given \(\overline{\mathbf{A E}}\) is a straight line.

Ratio of angles ∠1, ∠2, ∠3, ∠4 is 1 : 2 : 3 : 4 that is 1x: 2x: 3x: 4x

The sum of the angles at a point on the same side of the line is 180°

∠1 + ∠2 + ∠3 + ∠4 = 180°

⇒ 1x + 2x + 3x + 4x = 180°

⇒ 10x = 180

⇒ \(\frac{10 x}{10}=\frac{180}{10}\)

∴ x = 18°

2x = 2 × 18° = 36°

3x = 3 × 18° = 54°

4x = 4 × 18° = 72°

Therefore the angles are 18°, 36°, 54°, 72°.

Question 5.

Write any two examples for linear pair of angles in your surroundings.

Answer:

Electric pole, Tree/Pen stand, etc.

Question 6.

Mani said, “Two obtuse angles can form a pair of conjugate angles.” Do you agree? Justify your answer.

Answer:

Obtuse angle is always less than 180°. Sum of two obtuse angles is less than 360°.

So, I do not agree, that two obtuse angles cannot form a pair of conjugate angles.

Question 7.

Draw a pair of adjacent angles which are not supplementary to each other.

Answer:

(i)

∠AOB and ∠BOC are adjacent angles.

∠AOB + ∠BOC = 50° + 60°

= 110° ≠ 180°

∠AOB and ∠BOC are not supplementary.

(ii)

∠POQ and ∠QOR are adjacent angles.

∠POQ + ∠QOR = 70° + 80°

= 150° ≠ 180°

∠POQ and ∠QOR are not supplementary.

Question 8.

In the figure, if l ∥ m, t is a transversal. Find ∠1 and ∠2.

Answer:

Given l ∥ m and t is a transversal.

∠1 = 110° (vertically opposite angles)

∠1 + ∠2 = 180° (co-interior angles are supplementary)

110° + ∠2 = 180°

110° + ∠2 – 110° = 180° – 110°

∠2 – 70°

∠1 = 110° and ∠2 = 70°

Question 9.

A line p intersects two lines l and m at two distinct points. Observe the figure and fill in the blanks :

(i) The line ‘p’ is known as ________, ________

(ii) ∠1 and ∠5 is a pair of ________ angles.

(iii) ∠4 and ∠6 is a pair of ________ angles.

(iv) ∠3 and ∠6 is a pair of ________ angles.

Answer:

(i) transversal line,

(ii) corresponding

(iii) alternate interior

(iv) co-interior

Question 10.

In the given figure \(\overrightarrow{\mathbf{C F}} \| \overrightarrow{\mathbf{B D}}, \overrightarrow{\mathbf{B E}}\) is transversal. ∠CAE = 135°, then find ∠ABD

Answer:

Given \(\overrightarrow{\mathrm{CF}} \| \overrightarrow{\mathrm{BD}}\) and \(\overrightarrow{\mathrm{BE}}\) is transversal, ∠CAE — 135°

∠BAF = ∠CAE = 135° (vertically opposite angles)

∴ ∠BAF = 135°

∠BAF + ∠ABD = 180° (co-interior angles are supplementary)

135° + ∠ABD = 180°

135° + ∠ABD – 135° =180°- 135°

∴ ∠ABD = 45°