Page 143 - Start Up Mathematics_7

Solution: (a) Since, 35° + 55° = 90°, therefore the angles are complementary.
(b) Since, 48° + 52° = 100°, therefore the angles are not complementary.

Example 4: Find the complement of each of the following angles:

83° 57°
(a) (b)

Solution: (a) Let the complement of 83° be x. (b) Let the complement of 57° be x.
∴ x + 83° = 90° ∴ x + 57° = 90°
⇒ x = 7° ⇒ x = 33°

Example 5: The difference in the measures of two complementary angles is 20°. Find the measures
of the angles.
Solution: Let the measures of two angles be x and y.
We have, x + y = 90° ...(1) (Complementary angles)
also, x – y = 20° ...(2) (Given)
Adding (1) and (2) we get, 2x = 110°, i.e., x = 55°
⇒ y = 90° – x = 90° – 55° = 35°

Example 6: An angle is equal to four times its complement. Determine its measure.
Solution: Let the measures of the angle be x.
Complement of the given angle = 90° – x
Now, x = 4(90° – x) ( Angle = 4 complement)

⇒ x = 360° – 4x
⇒ 5x = 360° ⇒ x = 72°
Hence, the required angle measures 72°.

Supplementary Angles
Two angles are said to be supplementary, if the sum of their measures is 180°. For example,
∠A = 125° and ∠B = 55° are supplementary angles since their sum is 180°.

Example 7: Find which of the following pairs of angles are supplementary:

65° 50°

115° 130° 60° 60°

(a) (b) (c)

Solution: Two angles are said to be supplementary if the sum of their measures is 180°.
(a) Since, 115° + 65° = 180°, therefore the angles are supplementary.
(b) Since, 50° + 130° = 180°, therefore the angles are supplementary.
(c) Since, 60° + 60° = 120°, therefore the angles are not supplementary.

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