Page 156 - Maths Skills - 7

154 Maths

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Example 4: An angle is of its supplement. What is the measure of the angle?
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x
Solution: Let the supplement of the angle be x. Then, the angle is ·
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But sum of measure of an angle and its supplement is 180°.
x
\ + x = 180° Fact-o-meter
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x + 3x = 180º � Two acute angles or two obtuse angles can never
3 form a linear pair.
4x
or = 180° � Supplementary angles form a linear pair it they
3 are adjacent too.
or x = 180° × 3 = 135° � The sum of all the angles an a straight line is 180 °.
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\ The required angle is 135° = 45° � The sum of all the angles completing a rotation
3 about a point is 360°.

Exercise 9.1

1. State which of the following statements are true and which are false.
(i) Adjacent angles can be complementary. ________________

(ii) A pair of adjacent angles always forms a straight angle. ________________
(iii) The supplement of an acute angle is always an obtuse angle. ________________
(iv) The complement of 90° is 90°. ________________

(v) Two obtuse angles can be supplementary. ________________
(vi) Two complementary angles always form a linear pair. ________________
(vii) Vertically opposite angles are always equal. ________________

2. From figure, write the names of the: D C
(i) supplementary angles
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(ii) pairs of vertically opposite angles 3 1
E 4 5 B
(iii) angles which form linear pairs O
(iv) pairs of adjacent angles
A
3. Identify which of the following pairs of angles are complementary and which are supplementary.
(i) 63°, 27° (ii) 120°, 60° (iii) 45°, 135° (iv) 90°, 90° (v) 40°, 50°
4. Find the supplement of each of the following angles.

(i) 108° (ii) 78° (iii) 180° (iv) 135° (v) 145° (vi) 65°
5. Find the complement of each of the following angles.

(i) 35° (ii) 90° (iii) 45° (iv) 50° (v) 65° (vi) 68°
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6. Find the degree measure of an angle which is of its complement.
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7. Find the degree measure of an angle which is equal to its supplement.
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8. Find the degree measure of an angle which is of its supplement.
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