Class 6 - Mathematics
Chapter - Lines and Angles : Exercise 5.1
Top Block 1
Question: 1.Find the complement of each of the following angles:
Answer :
Complementary angle = 90° – given angle
(i) Complement of 20° = 90° – 20° = 70°
(ii) Complement of 63° = 90° – 63° = 27°
Complement of 57° = 90° – 57° = 33°
Question: 2.Find the supplement of each of the following angles:
Mddle block 1
Answer :
Supplementary angle = 180° – given angle
(i) Supplement of 105° = 180° – 105° = 75°
(ii) Supplement of 87° = 180° – 87° = 93°
Supplement of 154° = 180° – 154° = 26°
Question: 3.Identify which of the following pairs of angles are complementary and which are supplementary:
(i) 65°, 115°
(ii) 63°, 27°
(iii) 112°, 68°
(iv) 130°, 50°
(v) 45°, 45°
(vi) 80°, 10°
Answer :
If sum of two angles is 180°, then they are called supplementary angles.
If sum of two angles is 90°, then they are called complementary angles.
(i) 65°+115°=180° These are supplementary angles.
(ii) 63°+27°=90° These are complementary angles.
(iii) 112°+68°=180° These are supplementary angles.
(iv) 130°+50°=180° These are supplementary angles.
(v) 45°+45°=90° These are complementary angles.
(vi) 80°+10°=90° These are complementary angles.
Question: 4.Find the angle which is equal to its complement:
Answer :
Let one of the two equal complementary angles be x.
∴ x + x = 90°
⇒ 2x = 90°
⇒ x = 90°⁄2 = 45°
Thus, 45° is equal to its complement.
Question: 5.Find the angle which is equal to its supplement.
Answer :
Let x be two equal angles of its supplement.
Therefore, x + x = 180° [Supplementary angles]
⇒ 2x = 180°
⇒ x = 180°⁄2 = 90°
Thus, 90° is equal to its supplement.
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 :
I f∠1 is decreased then, ∠2 will increase with the same measure, so that both the angles still remain supplementary.
Question: 7.Can two angles be supplementary if both of them are:
(i) acute
(ii) obtuse
(iii) right?
Answer :
(i) No, because sum of two acute angles is less than 180°.
(ii) No, because sum of two obtuse angles is more than 180°.
(iii) Yes, because sum of two right angles is 180°.
Question: 8. An angle is greater than 45°. Is its complementary angle greater than 45° or equal to 45° or less than 45°?
Answer :
Let the complementary angles be x and y, i.e., x+y=90°
It is given that x > 45°
Adding y both sides, x+y > 45°+y
⇒ 90° > 45°+y ⇒ 90°–45° > y⇒ y < 45°
Thus, its complementary angle is less than 45°.
Question: 9.In the adjoining figure:
- Is ∠1 adjacent to ∠2?
- Is ∠AOC adjacent to ∠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 of ∠5?
Answer :
(i) Yes, in ∠AOE, OC is common arm.
(ii) No, they have no non-common arms on opposite side of common arm.
(iii) Yes, they form linear pair.
(iv) Yes, they are supplementary.
(v) Yes, they are vertically opposite angles.
(vi) Vertically opposite angles of ∠5 is ∠COB.
Question: 10.Indicate which pairs of angles are:
Linear pairs?
Answer :
(i) Vertically opposite angles, ∠1, ∠4; ∠5, ∠2 + ∠3.
(ii) Linear pairs ∠1, ∠5; ∠5, ∠4.
Question: 11.In the following figure, is ∠1 adjacent to ∠2? Give reasons.
Answer :
∠1 and ∠2 are not adjacent angles because their vertex is not common.
Question: 12.Find the values of the angles x,y and z in each of the following:
Answer :
(i) x = 55° [Vertically opposite angles]
Now 55° + y = 180° [Linear pair]
⇒ y = 180° – 55° = 125°
Also y = z = 125° [Vertically opposite angles]
Thus, x = 55°, y = 125° and z = 125°.
(ii) 40° + x + 25° = 180° [Angles on straight line]
⇒ 65° + x = 180°
⇒ x = 180° – 65° = 115°
Now 40° + y = 180° [Linear pair]
⇒ y = 180° – 40° = 140° ……….(i)
Also y + z = 180° [Linear pair]
⇒ 140° + z = 180° [From eq. (i)]
⇒ z = 180° – 140° = 40°
Thus, x = 115°, y = 140° 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 a linear pair are _______________.
- If two adjacent angles are supplementary, they form a _______________.
- If two lines intersect 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 :
(i) 90°
(ii) 180°
(iii) supplementary
(iv) linear pair
(v) equal
(vi) 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 :
(i) Obtuse vertically opposite angles means greater than 90° and equal ∠AOD = ∠BOC.
(ii) Adjacent complementary angles means angles have common vertex, common arm, non-common arms are on either side of common arm and sum of angles is 90°.
(iii) Equal supplementary angles means sum of angles is 180° and supplement angles are equal.
(iv) Unequal supplementary angles means sum of angles is 180° and supplement angles are unequal.
i.e., ∠AOE, ∠EOC; ∠AOD, ∠DOC and ∠AOB, ∠BOC
(v) Adjacent angles that do not form a linear pair mean, angles have common ray but the angles in a linear pair are not supplementary.
i.e., ∠AOB, ∠AOE; ∠AOE, ∠EOD and ∠EOD, ∠COD