SCERT AP 7th Class Maths Solutions Pdf Chapter 4 Lines and Angles Ex 4.3 Textbook Exercise Questions and Answers.

## AP State Syllabus 7th Class Maths Solutions 4th Lesson Lines and Angles Exercise 4.3

Question 1.

Name three pairs of vertically opposite angles in the figure. If ∠AOB = 45°, then find ∠DOE.

Answer:

Vertically opposite angles :

∠AOB, ∠DOE; ∠BOC, ∠EOF; ∠COD, ∠AOF

Given ∠AOB = 45°

In the given figure, ∠AOB is the vertically opposite angle to ∠DOE.

So, ∠DOE = ∠AOB = 45°

∴ ∠DOE = 45°

Question 2.

In the given figure \(\overrightarrow{\mathbf{PQ}}\) is a straight line. Check whether x and y are vertically opposite angles or not. Give reason.

Answer:

\(\overrightarrow{\mathbf{PQ}}\) is a straight line. But \(\overrightarrow{\mathbf{SR}}\) is not a straight line.

If \(\overrightarrow{\mathbf{PQ}}\) and \(\overrightarrow{\mathbf{SR}}\) are intersecting lines the x and y become vertically opposite angles.

So, x and y are not vertically opposite angles.

Question 3.

Write any three examples for vertically opposite angles in your surroundings.

Answer:

Scissors, window grills, cross roads, rail cross junctions, etc.

Question 4.

In the given figure, the lines l and m intersect at point P. Observe the figure and find the values of x, y and z.

Answer:

Given l and m are intersecting lines at P.

∠y = 20° (vertically opposite angles)

∠x = ∠z (vertically opposite angles)

∠y + ∠x = 180° (linear pair)

⇒ 20° + ∠x = 180°

⇒ 20° + ∠x – 20° = 180°- 20

⇒ ∠x = 160°

∴ ∠x = ∠z = 160°

∠x = 160°, ∠y = 20° and ∠z = 160°.

Question 5.

In the given figure, two lines \(\overleftrightarrow{\mathbf{A D}}\) and \(\overleftrightarrow{\mathbf{E C}}\) intersects at O. Name two pairs of vertically opposite angles in the given figure.

Answer:

In the given figure \(\overleftrightarrow{\mathbf{A D}}\) and \(\overleftrightarrow{\mathbf{E C}}\) are intersecting at O.

∠AOE = ∠COD (Vertically opposite angles)

∠1 = ∠3

∠EOD = ∠AOC (Vertically opposite angles)

∠EOD = ∠AOB + ∠BOC (we know ∠AOC = ∠AOB + ∠BOC)

∠2 = ∠5 + ∠4

Question 6.

Two lines \(\overleftrightarrow{\mathbf{P S}}\) and \(\overleftrightarrow{\mathbf{Q T}}\) intersect at M. Observe the figure and find x.

Answer:

In the given figure \(\overleftrightarrow{\mathbf{P S}}\) and \(\overleftrightarrow{\mathbf{Q T}}\) are intersecting at M.

∠PMQ = ∠TMS (Vertically opposite angles)

∠QMS = ∠PMT (Vertically opposite angles)

∠QMR + ∠RMS = ∠PMT (we know ∠QMS = ∠QMR + ∠RMS)

But, given, ∠QMR = 40°, ∠RMS = x° and ∠PMT = 105°

⇒ 40° + x° – 40° = 105° – 40°

∴ x° = 65°