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(i) (ii)

Answer :

From Fig. 1. we have

\(\angle \)x = 55° (Vertically opposite angles)

\(\angle \) x + \(\angle \) y = 180° (Adjacent angles)

55° + \(\angle \) y = 180° (Linear pair angles)

So, \(\angle \) y = 180° – 55° = 125°

\(\angle \) y = \(\angle \) z (Vertically opposite angles)

\(\angle \) z = 125 °

Hence, \(\angle \) x = 55°, \(\angle \) y = 125° and \(\angle \) z = 125°

From Fig. ii . we have

25° + x + 40° = 180° (Sum of adjacent angles on straight line)

65° + x = 180°

So, x = 180° – 65° = 115°

40° + y = 180° (Linear pairs)

So, y = 180° – 40° = 140°

y + z = 180° (Linear pairs)

140° + z = 180°

So, z = 180° – 140° = 40°

Hence, x – 115°, y = 140° and z – 40°

- Q.1 Find the complement of each of the following angles:
- Q.2 Find the supplement of each of the following angles:
- Q.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°
- Q.4 Find the angle which equal to its complement.
- Q.5 Find the angle which is equal to its supplement.
- Q.6 In the given figure, \(\angle \) 1 and \(\angle \)2 are supplementary angles. If \(\angle \) 1 is decreased, what changes should take place in \(\angle \) 2 so that both the angles still remain
- Q.7 Can two angles be supplementary if both of them are: (i) acute? (ii) obtuse? (iii) right?
- Q.8 An angle is greater than 45°. Is its complementary angle greater than 45° or equal to 45° or less than 45 °?
- Q.9 In the following figure: (i) Is \(\angle \)1 adjacent to angle 2? (ii) Is \(\angle \)AOC adjacent to angle AOE? (iii) Do \(\angle \) COE and \(\angle \) EOD form a linear pair? (iv) Are \(\angle \) BOD and \(\angle \) DOA supplementary? (v) Is \(\angle \) 1 vertically opposite angle to angle 4? (vi) What is the vertically opposite angle of \(\angle \) 5?
- Q.10 Indicate which pairs of angles are: (i) Vertically opposite angles (ii) Linear pairs
- Q.11 In the following figure, is \(\angle \)1 adjacent to \(\angle \)2? Give reasons.
- Q.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 ______ .
- Q.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.

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