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Complementary and Supplementary angles
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Complementary Angle Two angles are complementary if and only if the sum of their angle is 90. Example 1: Check if the pair of angle given below is complementary 50° H 40° Q P S Solution Given : PHQ=40 , QHS = 50 Step1:- Find the sum of pair of angles PHQ + QHS = = 90 Step2:- Check if the sum of pair of angles is 90 If the sum is 90 then the angles are complementary else it is not complementary ∴ Sum of pair of angles is 90, hence PHQ and QHS are complementary
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Example 2: Find whether the pair of angle below are complementary angles
Angle pair Sum of the angle Equal to 90 Complementary 20 and 50 20 + 50 = 70 no no 60 and 30 = 90 yes yes 40 and 40 40 + 40 = 80 no no 55 and 25 =90 yes yes 120 and 60 = 180 no no 13 and 67 13 + 67 = 90 yes yes
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Example 3: Find the complementary angle of 35
Solution We know that two angles are complementary if and only if the sum of their angle is 90. ∴ To find the complement, subtract the given angle from 90 90 – 35 = 55 Ans: The complementary angle of 35 is 55.
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Example 4: Find the complementary angle of given angle
- Complementary angle Complementary angle = 90 given angle Angle 45 90 – 45 45 30 90 – 30 60 20 90 – 20 70 10 90 – 10 80 70 90 – 70 20 60 90 – 60 30
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Supplementary Angle Two angles are supplementary if and only if the sum of their angle is 180. Example1: Check if the pair of angle given below is supplementary Solution Given : PHQ=130 , QHS = 50 50° H 130° Q P S Step1:- Find the sum of pair of angles PHQ + QHS = = 180 Step2:- Check if the sum of pair of angles is 180 If the sum is 180 then the angles are supplementary else it is not supplementary ∴ Sum of pair of angles is 90, hence PHQ and QHS are supplementary
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Example 2: Find whether the pair of angle below are supplementary angles
Angle pair Sum of the angle Equal to 180 Supplementary 110 and 50 = 160 no no 160 and 20 = 180 yes yes 70 and 140 = 210 no no 135 and 45 =180 yes yes 40 and 50 = 90 no no 145 and 35 = 180 yes yes
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Example 3: Find the supplementary angle of 130
Solution We know that two angles are supplementary if and only if the sum of their angle is 180. ∴ To find the complement, subtract the given angle from 180 180 – 130 = 50 Ans: The supplementary angle of 130 is 55.
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Example 5: Find the Complementary and Supplementary angle of given angle
- Supplementary angle Supplementary angle = 180 given angle Angle 100 180 - 100 80 60 180 - 60 120 120 180 - 120 60 30 180 - 30 150 90 180 - 90 90 140 180 - 140 40
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Example 2: Find whether the pair of angle below are supplementary angles
90 - Complementary angle = given angle Supplementary angle = 90 - given angle Angle 35 – 90 35 = 55 – 180 35 = 145 Given angle >90, so no complementary angle possible 120 – 180 120 = 60 70 – 90 70 = 20 – 180 70 = 110 80 – 90 80 = 10 – 180 80 = 100 Given angle >90, so no complementary angle possible 150 – 180 150 = 30 20 – 90 20 = 70 – 180 20 = 60
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Try these 1. Find the supplement angle of 112°? 2. Find the complement angle of 63°?
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