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Chapter 5 Lines and Angles Ex 5.1 Solutions

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

Answer - 11 : -

No, ∠1 and∠2 are not adjacent angles.

Reasons:
(i) ∠1 + ∠2 ≠ 180°
(ii) They have no common vertex.

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

Answer - 12 : -

From Fig. 1. we have
∠x = ∠55° (Vertically opposite angles)
∠x + ∠y = 180° (Adjacent angles)
55° + ∠y = 180° (Linear pair angles)
∴ ∠y = 180° – 55° = 125°
∠y = ∠z (Vertically opposite angles)
125° = ∠z
Hence, ∠x = 55°, ∠y = 125° and ∠z = 125°
(ii) 25° + x + 40° = 180° (Sum of adjacent angles on straight line)
65° + x = 180°
∴ x = 180° – 65° = 115°
40° + y = 180° (Linear pairs)
∴ y = 180° – 40° = 140°
y + z = 180° (Linear pairs)
140° + z = 180°
∴ z = 180° – 140° = 40°
Hence, x – 115°, y = 140° and z – 40°

Question - 13 : -
Fill in the blanks:
(i) If two angles are complementary, then the sum of their measures is ______ .
(ii) If two angles are supplementary, then the sum of their measures is ______ .
(iii) Two angles forming a linear pair are ______ .
(iv) If two adjacent angles are supplementary, they form a ______ .
(v) If two lines intersect at a point, then the vertically opposite angles are always ______ .
(vi) 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 - 13 : -

(i) 90°
(ii) 180°
(iii) Supplementary
(iv) Linear pair
(v) Equal
(vi) Obtuse angle

Question - 14 : -
In the given figure, name the following pairs of angles.
 
(i) Obtuse vertically opposite angles.
(ii) Adjacent complementary angles.
(iii) Equal supplementary angles.
(iv) Unequal supplementary angles.
(v) Adjacent angles but do not form a linear pair.

Answer - 14 : -

(i) ∠BOC and∠AOD areobtuse vertically opposite angles.
(ii) ∠AOB and∠AOE areadjacent complementary angles.
(iii) ∠EOB and∠EOD areequal supplementary angles.
(iv) ∠EOA and∠EOC areunequal supplementary angles.
(v) ∠AOB and∠AOE, ∠AOE and ∠EOD, ∠EOD and∠COD areadjacent angles but do not form a linear pair.

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