Find the measure of an angle which is

Question:

Find the measure of an angle which is
(i) equal to its complement
(ii) equal to its supplement

Solution:

(i) Let the measure of the required angle be $x^{\circ}$.

Then, in case of complementary angles:

$x+x=90^{\circ}$

$\Rightarrow 2 x=90^{\circ}$

$\Rightarrow x=45^{\circ}$

Hence, measure of the angle that is equal to its complement is $45^{\circ}$.

(ii) Let the measure of the required angle be $x^{\circ}$

Then, in case of supplementary angles:

$x+x=180^{\circ}$

$\Rightarrow 2 x=180^{\circ}$

$\Rightarrow x=90^{\circ}$

Hence, measure of the angle that is equal to its supplement is $90^{\circ}$.

 

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