# Lines & Angles

## Exercise 5.1

Question 1: Find the complement of each of the following angles:

**Answer:** (i) 70°, (ii) 27°, (iii) 33°

Question 2: Find the supplement of each of the following angles:

**Answer:** (i) 75°, (ii) 93°, (iii) 26°

Question 3: Identify which of the following pairs of angles are complementary and which are supplementary.

- 65°, 115°
- 63°, 27°
- 112°, 68°
- 130°, 50°
- 45°, 45°
- 80°, 10°

**Answer:** (i) Supplementary, (ii) Complementary, (iii) Supplementary, (iv) Supplementary, (v) Complementary, (vi) Complementary

Question 4: Find the angle which is equal to its complement.

**Answer:** 45° (As is clear from option (v) of previous question)

Question 5: Find the angle which is equal to its supplement.

**Answer:** 90°

Question 6: In the given figure, ∠1 and ∠2 are supplementary angles. If ∠1 is decreased, what changes should take place in ∠2 so that both the angles still remain supplementary?

**Answer:** ∠2 should increase

Question 7: Can two angles be supplementary if both of them are:

- Acute
- Obtuse
- Right

**Answer:** (i) No, (ii) No, (iii) Yes

Question 8: An angle is greater than 45°. Is its complementary angle greater than 45° or equal to 45° or less than 45°?

**Answer:** Less than 45°

Question 9: In the adjoining figure:

- Is ∠1 adjacent to ∠2?
- Is ∠AOC adjacent to &agnle;AOE?
- Do ∠COE and ∠EOD form a linear pair?
- Are ∠BOD and ∠DOA supplementary?
- Is ∠1 vertically opposite to ∠4?
- What is the vertically opposite angle to ∠5?

**Answer:** (i) Yes, (ii) No, (iii) Yes, (iv) Yes, (v) Yes, (vi) Sum of °3 and °3

Question 10: Indicate which pairs of angles are:

- Vertically opposite angles
- Linear pairs

**Answer:** (i) ∠1 and ∠4 (ii) ∠5 and ∠1 & ∠5 and ∠4

Question 11: In the following figure, is °1 adjacent to °2? Give reasons.

**Answer:** They do not have common vertex. So, they are not adjacent angles.

Question 12: Find the values of angles x, y and z in each of the following:

**Answer:** (i) `∠x-55°` (Vertically opposite angles)

`∠x+∠y=180°` (Linear pair of angles)

Or, `∠y+55°=180°`

Or, `∠y=180-55=125°`

Now, `∠z=∠y` (Vertically opposite angles)

So, `∠x=125°`

Thus, `x=55°`, `y=125°` and `z=125°`

**Answer:** (ii) `∠z=40°` (Vertically opposite angles)

`∠40°+x+25°=180°` (Angles on same side of a line)

So, `∠x=180-(40+25)=180-65=115°`

Now, `∠y=∠x=115°` (Vertically opposite angles)

Thus, `x=115°`, `y=115°` and `z=40°`

Question 13: Fill in the blanks:

- If two angles are complementary, then the sum of their measures is …………………
- If two angles are supplementary, then the sum of their measures is ………………..
- Two angles forming linear pair are …………………..
- If two adjacent angles are supplementary, they form a ………………………
- If two lines intersect at a point, then the vertically opposite angles are always ……………………
- If two lines intersect at a point, and if one pair of vertically opposite angles are acute angles, then the other pair of vertically opposite angles are …………………………..

**Answer:** (a) 90°, (b) 180°,(c) Supplementary, (d) Linear pair, (e) equal, (f) Obtuse angles

Question 14: In the adjoining figure, name the following pairs of angles.

- Obtuse vertically opposite angles
- Adjacent complementary angles
- Equal supplementary angles
- Unequal supplementary angles
- Adjacent angles that do not form a linear pair

**Answer:** (a) ∠AOD and ∠BOC, (b) ∠AOB and ∠AOE, (c) ∠BOE and ∠EOD, (d) ∠AOE and ∠EOC, (e) ∠EOD and ∠DOC