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 $90^{\circ}$.
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.