## Chapter 2 Parallel Lines and Transversals 2.2

Question 1.

Choose the correct alternative.

i. In the given figure, if line m || line n and line p is a transversal, then find x.

(A) 135°

(B) 90°

(C) 45°

(D) 40°

Solution:

(C) 45°

Hint:

ii. In the given figure, if line a || line b and line l is a transversal, then find x.

(A) 90°

(B) 60°

(C) 45°

(D) 30°

Solution:

(D) 30°

Hint:

Question 2.

In the given figure, line p || line q. Line t and line s are transversals. Find measure of ∠x and ∠y using the measures of angles given in the figure.

Solution:

i. Consider ∠z as shown in figure.

line p || line q and line t is a transversal.

∴ m∠z = 40° …(i) [Corresponding angles]

m∠x + m∠z = 180° …[Angles in a linear pair]

∴ m∠x + 40o = 180° …[From(i)]

∴ m∠x= 180° – 40°

∴ m∠x = 140°

ii. Consider ∠w as shown in the figure.

m∠w + 70° = 180° …[Angles in a linear pair]

∴ m∠w = 180° – 70°

∴ m∠w = 110° …(ii)

line p || line q and line s is a transversal.

∴ m∠y = m∠w …[Alternate angles]

∴ m∠y =110° …[From (ii)]

∴ m∠x = 140°, m∠y = 110°

Question 3.

In the given figure, line p || line q, line l || line m. Find measures of ∠a, ∠b and ∠c, using the measures of given angles. Justify your answers.

Solution:

i. line p || line q and line l is a transversal.

∴ m∠a + 80° = 180° …[Interior angles]

∴ m∠a= 180° – 80°

∴ m∠a= 100°

ii. line l || line m and line p is a transversal.

∴ m∠c = 80° …(i) [Exterior alternate angles]

iii. line p || line q and line m is a transversal.

∴ m∠b = m∠c … [Corresponding angles]

m∠b = 80° …[From (i)]

∴ m∠a = 100°, m∠b = 80°, m∠c = 80°

Question 4.

In the given figure, line a || line b, line l is a transversal. Find the measures of ∠x, ∠y, ∠z using the given information.

Solution:

line a || line b and line l is a transversal.

∴ m∠x = 105° …(i) [Corresponding angles]

ii. m∠y = m∠x … [Vertically opposite angles]

∴ m∠y = 105° …[From (i)]

iii. m∠z + 105° = 180° …[Angles in a linear pair]

∴ m∠z = 180°- 105°

∴ m∠z = 75°

∴ m∠x = 105°, m∠y = 105°, m∠z = 75°

Question 5.

In the given figure, line p || line l || line q. Find ∠x with the help of the measures given in the figure.

Solution:

line p || line l and line IJ is a transversal.

m∠IJN = m∠JIH … [Alternate angles]

∴ m∠IJN = 40° …(i)

line l || line q and line MJ is a transversal.

m∠MJN = m∠JMK … [Alternate angles]

∴ m∠MJN = 30° …(ii)

Now, m∠x = m∠IJN + m∠MJN

…[Angle addition property]

= 40° + 30° …[From (i) and (ii)]

∴ m∠x = 70°

**Intext Questions and Activities**

Question 1.

When two parallel lines are intersected by a transversal eight angles are formed. If the measure of one of these eight angles is given, can we find measures of remaining seven angles? (Textbook pg, no. 9)

Solution:

Yes, we can find the measures of the remaining angles.

In the given figure, line m || line n and line l is a transversal.

m∠a = 60°(say) …(i)

i. m∠a + m∠b = 180° …[Angles in a linear pair]

∴ 60° + m∠b =180° … [From (i)]

∴ m∠b = 180° – 60°

∴ m∠b = 120° …(ii)

ii. m∠c = m∠b …[Vertically opposite angles]

∴ m∠c = 120° .. .(iii) [From (ii)]

iii. m∠d = m∠a …[Vertically opposite angles]

∴ m∠d = 60° …(iv) [From (i)]

iv. m∠e = m∠d …[Alternate angles]

∴ m∠e = 60° … [From (iv)]

v. m∠f = m∠c …[Alternate angles]

∴ m∠f = 120° …[From (iii)]

vi. m∠g = m∠d …[Corresponding angles]

∴ m∠g = 60° … [From (iv)]

vii. m∠h = m∠c … [Corresponding angles]

∴ m∠h = 120° …[From (iii)]

Question 2.

As shown in the figure (A), draw two parallel lines and their transversal on a paper. Draw a copy of the figure on another blank sheet using a trace paper, as shown in the figure (B). Colour part Land part II with different colours. Cut out the two parts with a pair of scissors. Place, part I and part II on each angle in the figure A and answer the following questions. (Textbook pg. no. 9)

- Which angles coincide with part I?
- Which angles coincide with part II?

Solution:

- ∠d, ∠f and ∠h coincide with part I.
- ∠c, ∠e and ∠g coincide with part II.