Lines & Angles

Exercise 5.1

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

lines and angles lines and angles lines and angles

Answer: (i) 70°, (ii) 27°, (iii) 33°

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

lines and angles lines and angles lines and angles

Answer: (i) 75°, (ii) 93°, (iii) 26°

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

  1. 65°, 115°
  2. 63°, 27°
  3. 112°, 68°
  4. 130°, 50°
  5. 45°, 45°
  6. 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?

lines and angles

Answer: ∠2 should increase

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

  1. Acute
  2. Obtuse
  3. 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:

lines and angles
  1. Is ∠1 adjacent to ∠2?
  2. Is ∠AOC adjacent to &agnle;AOE?
  3. Do ∠COE and ∠EOD form a linear pair?
  4. Are ∠BOD and ∠DOA supplementary?
  5. Is ∠1 vertically opposite to ∠4?
  6. 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:

lines and angles
  1. Vertically opposite angles
  2. 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.

lines and angles

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:

lines and angles lines and angles

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:

  1. If two angles are complementary, then the sum of their measures is …………………
  2. If two angles are supplementary, then the sum of their measures is ………………..
  3. Two angles forming linear pair are …………………..
  4. If two adjacent angles are supplementary, they form a ………………………
  5. If two lines intersect at a point, then the vertically opposite angles are always ……………………
  6. 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.

lines and angles
  1. Obtuse vertically opposite angles
  2. Adjacent complementary angles
  3. Equal supplementary angles
  4. Unequal supplementary angles
  5. 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

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