SCERT AP 7th Class Maths Solutions Pdf Chapter 4 Lines and Angles Ex 4.4 Textbook Exercise Questions and Answers.

AP State Syllabus 7th Class Maths Solutions 4th Lesson Lines and Angles Exercise 4.4

Question 1.
In the given figure, two lines p ∥ q arid r is transversal, If ∠3 = 135°, then find the remaining angles.
AP Board 7th Class Maths Solutions Chapter Chapter 4 Lines and Angles Ex 4.4 1
Answer:
Given ∠3 = 135
∠1 = ∠3 = 135° (vertically opposite angles)
∠1 = ∠5 = 135° (corresponding angles)

∠3 = ∠8 = 135° (corresponding angles)
∠3 = ∠5 = 135° (Alternate interior angles)

∠1 + ∠7 = 180° (co-exterior angles are supplementary)
135° + ∠7 = 180°
∠7 = 180°- 135° = 45°
∠6 = ∠7 = 45° (vertically opposite angles)
∠6 = ∠2 = 45° (corresponding angles)
∠4 = ∠7 = 45° (corresponding angles)
∴ ∠1 = 135°, ∠2 = 45°, ∠3 = 135°, ∠4 = 45°, ∠5 = 135°, ∠6 = 45°, ∠7 = 45°, ∠8 = 135°

Question 2.
In the given figure, \(\overleftrightarrow{\mathbf{AB}}\) || \(\overleftrightarrow{\mathbf{CD}}\) and \(\overleftrightarrow{\mathbf{DE}}\) is a transversal. Find x.
AP Board 7th Class Maths Solutions Chapter Chapter 4 Lines and Angles Ex 4.4 2
Answer:
Given \(\overleftrightarrow{\mathbf{AB}}\) || \(\overleftrightarrow{\mathbf{CD}}\) and \(\overleftrightarrow{\mathbf{DE}}\) is a transversal line.
∠ABE = ∠CDB (corresponding angles)
∠ABF + ∠FBE = ∠CDB (we know ∠ABE = ∠ABF + ∠FBE)
From the figure ∠ABF = 35°,
∠FBE = x° and ∠CDB =100°
35° + x = 100°
⇒ 35° + x – 35° = 100° – 35°
∴ x = 65°

AP Board 7th Class Maths Solutions Chapter 4 Lines and Angles Exercise 4.4

Question 3.
In the given figure, m || n and p is transversal. Find x and y.
AP Board 7th Class Maths Solutions Chapter Chapter 4 Lines and Angles Ex 4.4 3
Answer:
Given m || n and p is transversal.
So, ∠x = 120° (vertically opposite angles)
45 + y = x (corresponding angles)
⇒ 45 + y = 120° (we know ∠x = 120°)
⇒ 45 + y – 45 = 120-45°
⇒ y = 75°
x = 120° and y = 75°

Question 4.
In the given figure, \(\overrightarrow{\mathbf{A B}}\|\overrightarrow{\mathbf{C D}}\| \overrightarrow{\mathbf{F E}}\). Find x, y and ∠AEC.
AP Board 7th Class Maths Solutions Chapter Chapter 4 Lines and Angles Ex 4.4 4
Answer:
Given \(\overrightarrow{\mathbf{A B}}\|\overrightarrow{\mathbf{C D}}\| \overrightarrow{\mathbf{F E}}\)
∠x = 20° (Alternate interior angles)
∠y = 33° (Alternate interior angles)
∠AEC = ∠AEF + ∠FEC
∠AEC = ∠x + ∠y
∠AEC = 20° + 33° = 53°
∴ x = 20°, y = 33° and ∠AEC = 53°

Question 5.
In the given figure, a transversal t intersects two lines p and q. Check whether p ∥q or not.
AP Board 7th Class Maths Solutions Chapter Chapter 4 Lines and Angles Ex 4.4 5
Answer:
If co-interior angles are supplementary, then the lines are parallel.
100° + 80° = 180° (co-interior angles supplementary)
So, p and q are parallel to each other.

Question 6.
In the given figure if l ∥m, then find x, y and z.
AP Board 7th Class Maths Solutions Chapter Chapter 4 Lines and Angles Ex 4.4 6
Answer:
Given l ∥m and AC is transversal.
z = 40° (Alternate interior angles)
l ∥m and AB is transversal. , and x + (y + z) = 180° (co-interior angles are supplementary)
x + y + z = 180°
(x + y) + 40° = 180° (co-interior angles are supplementary) (∵ z = 40°)
x + y + 40° = 180°
x + y + 40°-40° = 180° – 40°
∴ x + y = 140°
But x = y (given)
2x = 140°
∴ x = \(\frac{140^{\circ}}{2}\) = 70° = y
So, x = 70°, y = 70° and z = 40°

AP Board 7th Class Maths Solutions Chapter 4 Lines and Angles Exercise 4.4

Question 7.
In the given figure p, q, r and s are parallel lines and t is a transversal. Find x, y and z.
AP Board 7th Class Maths Solutions Chapter Chapter 4 Lines and Angles Ex 4.4 7
Answer:
p ∥ q
So, 80° + x = 180° (co-interior angles)
80° + x-80° = 180°-80°
x = 100°

q ∥ r
x + y = 180° (co-interior angles)
100° + y = 180° (we know x – 100°)
100° + y – 100° = 180°- 100°
y = 80°

r∥s
y = z (Alternate exterior angles)
y = z = 80° (we know y = 80°)
x = 100°, y = 80° and z = 80°

Question 8.
In the given figure \(\overrightarrow{\mathbf{A B}} \| \overrightarrow{\mathbf{C D}}\) and E is a point in between them. Find x + y + z. (Hint : Draw a parallel line to \(\overrightarrow{\mathbf{A B}}\) through E)
AP Board 7th Class Maths Solutions Chapter Chapter 4 Lines and Angles Ex 4.4 8
Answer:
Given \(\overrightarrow{\mathbf{A B}} \| \overrightarrow{\mathbf{C D}}\)
AP Board 7th Class Maths Solutions Chapter Chapter 4 Lines and Angles Ex 4.4 9
Draw \(\overrightarrow{\mathrm{EF}} \| \overrightarrow{\mathrm{AB}}\)
∠BAE = x,
∠AEF = p
∠FEC = q,
∠ECD = z
∠AEC = ∠AEF + ∠FEC
y = p + q

AB ∥ EF and AE is a transversal.
∠BAE + ∠AEF = 180° (co-interior angles are supplementary)
x + p = 180° ……………….(1)
CD ∥ EF and EC is a transversal.
∠FEC + ∠ECD = 180° (co-interior angles are supplementary’)
q + z = 180° …………….(2)

By adding (1) and (2)
AP Board 7th Class Maths Solutions Chapter Chapter 4 Lines and Angles Ex 4.4 10
x + y. + z = 360° (we know y = p + q)

Question 9.
Identify the pair of parallel lines in the given figure and write them.
AP Board 7th Class Maths Solutions Chapter Chapter 4 Lines and Angles Ex 4.4 11
Answer:
∠A = ∠E = 60° So, AL ∥ EH
∠B = ∠D = 90° So, BK ∥ DL
∠C = ∠F = 50° So, CJ ∥FG