Book Online Demo

Check Your IQ

Try Test

Courses

Offline Centres

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

see full answer

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

135^{o}

120^{o}

60^{o}

45^{o}

answer is D.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

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.

Watch 3-min video & get full concept clarity