Mathematics

# Mark the correct alternative of the following.The sum of an angle and one third of its supplementary angle is $90^o$. The measure of the angle is?

$45^o$

##### SOLUTION
Let, required angle be $A$ and its supplementary angle be $B$.
$\therefore \angle A+\angle B=180^0$
$\therefore \angle B=180^0-\angle A$
According to condition, the sum of an angle and one third of its supplementary angle is $90^0$
$\angle A+\dfrac{1}3\angle B=90^0\\$
$\angle A+\dfrac{1}3(180^0-\angle A)=90^0\\$
$\dfrac2{3}\angle A+60^0=90^0\\$
$\dfrac2{3}\angle A=30^0\\$
$\angle A=45^0\\$
$\therefore$ measure of a required angle is $45^0$

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Single Correct Medium Published on 09th 09, 2020
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