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The sum of an angle and one third of its supplementary angle is $90^{o}$ . The measure of the angle is?

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135^{o}

120^{o}

60^{o}

45^{o}

answer is D.

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Detailed Solution

It is given that the sum of an angle and one third of its supplementary angle is

90^{o}

.
Two angles are said to be supplementary angles when they add up to 180°.
Let, the required angle be

x

and its supplementary angle be

(180 - x)

∴ ∠ x + ∠ (180 - x) = 180^{0}

According to the given data, the sum of an angle and one third of its supplementary angle is

90^{0}

.
So we get the equation as follows.

∠ x + \frac{1}{3} ∠ (180 - x) = 90^{0}

\Rightarrow \frac{2}{3} ∠ x + 60^{0} = 90^{0}

\Rightarrow \frac{2}{3} ∠ x = {90^{0} - 60}^{0}

\Rightarrow \frac{2}{3} ∠ x = 30^{0}

\Rightarrow ∠ x = \frac{3}{2} \times 30 °

\Rightarrow ∠ x = \frac{90 °}{2}

\Rightarrow ∠ x = 45^{0}

∴

Measure of a required angle is

45^{0} .

Therefore, option 4 is the right answer.

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