Mathematics

# Mark the correct alternative of the following.The sum of an angle and half of its complementary angle is $75^o$. The measure of the angle is?

$60^o$

##### SOLUTION
Two Angles are Complementary when they add up to $90^0$
Let, $A$ and $B$ be the angles.
$\therefore \angle A+\angle B=90^0$
$\therefore \angle A=90^0-\angle B$       ...$(1)$
According to condition, the sum of an angle and half of its complementary angle is $75^0$
$\angle A+\dfrac1{2}\angle B=75^0$
$\therefore 90^0-\angle B+\dfrac1{2}\angle B=75^0\\$
$\therefore 90^0-\dfrac1{2}\angle B=75^0\\$
$\therefore 90^0-75^0=\dfrac1{2}\angle B\\$
$\therefore 15^0=\dfrac1{2}\angle B\\$
$\therefore \angle B=30^0\\$
$\therefore \angle A=60^0$
Therefore, measure of the required angle is $60^0$

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Single Correct Medium Published on 09th 09, 2020
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