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.

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.

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°

Question 3.

In the given figure, m || n and p is transversal. Find x and y.

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.

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.

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.

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°

Question 7.

In the given figure p, q, r and s are parallel lines and t is a transversal. Find x, y and z.

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)

Answer:

Given \(\overrightarrow{\mathbf{A B}} \| \overrightarrow{\mathbf{C D}}\)

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)

x + y. + z = 360° (we know y = p + q)

Question 9.

Identify the pair of parallel lines in the given figure and write them.

Answer:

∠A = ∠E = 60° So, AL ∥ EH

∠B = ∠D = 90° So, BK ∥ DL

∠C = ∠F = 50° So, CJ ∥FG