Complementary : GMAT Problem Solving (PS)
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# Complementary

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Joined: 10 Nov 2010
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24 Feb 2011, 09:07
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Whats the rule for complementary angles.
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24 Feb 2011, 09:23
Precisely as mentioned in the example; Pair of angles that sum to $$90^{\circ}$$ is called complementary. Pair of angles that sum to $$180^{\circ}$$ are called supplementary.

e.g.
$$\angle{a}=45^{\circ}$$
What will be its complementary angle: Clearly 90-45=$$45^{\circ}$$

$$\angle{a}=1^{\circ}$$
What will be its complementary angle: Clearly 90-1=$$89^{\circ}$$

$$\angle{a}=120^{\circ}$$
What will be its supplementary angle: Clearly 180-120=$$60^{\circ}$$

$$\angle{a}=1^{\circ}$$
What will be its supplementary angle: Clearly 180-1=$$179^{\circ}$$

; For this figure;
a and b are complementary angles;
Means a+b=90;

e+d will also be 90(complementary). If two lines intersect each other the opposite angles will always be equal.
In this figure; "e+d" is the opposite to "a+b"

a+e will also be complementary. (a+b is complementary; and e=b; opposite angles)
Likewise
b+d will also be complementary. (b+a is complementary; and a=d; opposite angles)
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Re: Complementary   [#permalink] 24 Feb 2011, 09:23
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