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Question
Two complementary angles are such that two times the measure of one is equal to three times the measure of the other. The measure of the smaller angle is
Options
45°
30°
36°
none of these
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Solution
Let one angle be x°.
Then, the other complementary angle becomes (90 - x)°
It is given that two times the angle measuring x°is equal to three times the angle measuring (90 - x)°
Or, we can say that:
2x = 3(90 - x)
2x = 270 - 3x
2x + 3x = 270
5x = 270
On dividing both sides of the equation by 5,we get
`x = 270/5`
x = 54
Also, the other complementary angle becomes
90 - x = 90 - 54
= 36
Thus, the measure of the required smaller angle is 36°.
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