Question

If the angle and its complement are x° and √x° respectively, find the angle.​

Answer 1

Answer:

Question-

If the angle and its complement are x° and √x° respectively, find the angle.

Solution -

Sum of the two angles Should be 90°

Complementary angles , x + √x = 90°.

putting,

$\mathrm{x =y^2}$

The Equation reduces to

${y}^{2} + y = 90$

${y}^{2} + y - 90 = 0$

${y}^{2} + 10y - 9y - 90 = 0$

$y(y + 10) - 9(y + 10) = 0$

$(y + 10)(y - 9) = 0$

$y = - 10 \: and \: 9$

Since y can't have negative value ,

y = 9 is only acceptable Solution.

$x = {9}^{2} = 81$

Hence, the required angle is 81°.

Answer 2

Answer:

Question-

If the angle and its complement are x° and √x° respectively, find the angle.

Solution -

Sum of the two angles Should be 90°

Complementary angles , x + √x = 90°.

putting,

$\mathrm{x =y^2}$

The Equation reduces to

${y}^{2} + y = 90$

${y}^{2} + y - 90 = 0$

${y}^{2} + 10y - 9y - 90 = 0$

$y(y + 10) - 9(y + 10) = 0$

$(y + 10)(y - 9) = 0$

$y = - 10 \: and \: 9$

Since y can't have negative value ,

y = 9 is only acceptable Solution.

$x = {9}^{2} = 81$

Hence, the required angle is 81°.

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