Complementary Angles (āĻĒā§‚ā§°āĻ• āϕ⧋āĻŖ) // Adjacent complementary angles. (āϏāĻ¨ā§āύāĻŋāĻšāĻŋāϤ āĻĒā§‚ā§°āĻ• āϕ⧋āĻŖāĨ¤


Complementary Angles (āĻĒā§‚ā§°āĻ• āϕ⧋āĻŖ)


Two angles are said to be complementary if the sum of their measures is 90°. Each angle is called the complement of the other.
āϝāĻŋ āĻĻ⧁āϟāĻž āϕ⧋āĻŖā§° āϝ⧋āĻ—āĻĢāϞ 90° āĻšāϝāĻŧ, āϏ⧇āχ āϕ⧋āĻŖāϝ⧋⧰āĻ• āĻĒā§‚ā§°āĻ• āϕ⧋āĻŖ (Complementary Angles) āĻŦā§‹āϞāĻž āĻšāϝāĻŧāĨ¤ āĻĒā§ā§°āϤāĻŋāĻŸā§‹ āϕ⧋āĻŖ āφāύāĻŸā§‹ā§° āĻĒā§‚ā§°āĻ•āĨ¤


Ex 1 | āωāĻĻāĻžāĻšā§°āĻŖ ā§§


Are 30° and 60° complementary ?
30° āφ⧰⧁ 60° āĻĒā§‚ā§°āĻ• āύ⧇āĻ•āĻŋ ?


Solution | āϏāĻŽāĻžāϧāĻžāύ:
30° + 60° = 90°
So, they are complementary angles.
āϏ⧇āϝāĻŧ⧇, āĻāχ āĻĻ⧁āϟāĻž āĻĒā§‚ā§°āĻ• āϕ⧋āĻŖāĨ¤


Ex 2 | āωāĻĻāĻžāĻšā§°āĻŖ ⧍


Adjacent complementary angles. (āϏāĻ¨ā§āύāĻŋāĻšāĻŋāϤ āĻĒā§‚ā§°āĻ• āϕ⧋āĻŖāĨ¤)


40° + 50° = 90°


Problem | āϏāĻŽāĻ¸ā§āϝāĻž


Find the complement of 70°. (70°-ā§° āĻĒā§‚ā§°āĻ• āϕ⧋āĻŖ āύāĻŋā§°ā§āĻŖāϝāĻŧ āϕ⧰āĻ•āĨ¤)


Solution | āϏāĻŽāĻžāϧāĻžāύ:
Complement = 90° − 70° = 20°


Ans | āωāĻ¤ā§āϤ⧰: 20°


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MCQs 


1. Two angles are complementary if their sum is ______. / āĻĻ⧁āϟāĻž āϕ⧋āĻŖā§° āϝ⧋āĻ—āĻĢāϞ ______ āĻšāϞ⧇ āϏāĻŋāĻšāρāϤ āĻĒā§‚ā§°āĻ• āϕ⧋āĻŖ āĻšāϝāĻŧāĨ¤
(a) 90° (b) 180° (c) 270° (d) 360°
Ans: (a) 90°


2. Which of the following is a pair of complementary angles ? / āϤāϞ⧰ āϕ⧋āύāĻŸā§‹ āĻĒā§‚ā§°āĻ• āϕ⧋āĻŖāϝ⧋⧰ ?
(a) 30°, 60° (b) 80°, 40° (c) 45°, 60° (d) 50°, 50°
Ans: (a) 30°, 60°


3. The complement of 70° is ______. / 70°-ā§° āĻĒā§‚ā§°āĻ• āϕ⧋āĻŖ āĻ•āĻŋāĻŽāĻžāύ ?
(a) 10° (b) 20° (c) 30° (d) 40°
Ans: (b) 20°


4. If one complementary angle is 35°, the other angle is ______. / āϝāĻĻāĻŋ āĻāϟāĻž āĻĒā§‚ā§°āĻ• āϕ⧋āĻŖ 35° āĻšāϝāĻŧ, āφāύāĻŸā§‹ āϕ⧋āĻŖ āĻ•āĻŋāĻŽāĻžāύ ?
(a) 45° (b) 55° (c) 65° (d) 75°
Ans: (b) 55°


5. Adjacent complementary angles have a sum of ______. / āϏāĻ¨ā§āύāĻŋāĻšāĻŋāϤ āĻĒā§‚ā§°āĻ• āϕ⧋āĻŖā§° āϝ⧋āĻ—āĻĢāϞ ______āĨ¤
(a) 90° (b) 180° (c) 270° (d) 360°
Ans: (a) 90°