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If the difference of two complementary angles is $30^{o}$ then, determine the two angles.

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60^{o}, 30^{o}

70^{o}, 40^{o}

20^{o}, 50^{o}

105^{o}, 75^{o}

answer is A.

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Detailed Solution

Given, the difference of two complementary angles is

30^{o}

.
Let

x

and

y

be the angles.
Then,

x + y = 90^{o} . . . . (1)

… (complementary angles).
Also,

x - y = 30^{o} . . . . (2)

… (given).
By addition of both equations, we get,

2 x = 120^{o}

⇒

x = \frac{120^{o}}{2}

⇒

x = 60^{o}

.
Putting the value of

x

in equation

(1)

, we get,

60 + y = 90^{o}

⇒

y = 90^{o} - 60^{o}

⇒

y = 30^{o}

Therefore, the required angles are

30^{o}

and

60^{o}

.
Hence, the correct option is 1.

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