Question

find the measure of an angle which is 1) equal to its complement 2) equal to its supplement

Answer 1

$\bold{\boxed{Solution:}}$

1) Let the measure of an angle be x.

And it's complement = (90- x).

$\bold{\boxed{A.T.Q}}$

x = 90 - x

=> x + x = 90

=> 2x = 90

=> x = 90/2

=> x = 45°

Therefore, the measure of required angle is 45°.
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2) Let the measure of an angle be x.

And it's supplement = (180 - x)

$\bold{\boxed{A.T.Q}}$

x = 180 - x

=> x + x = 180

=> 2x = 180

=> x = 180/2

=> x = 90°

Therefore, the measure of required angle is 90°.

$\bold{\boxed{Thank you!!}}$

Answer 2

$\large{\underline{\bold{Solution:}}}$


$\bold{Soln: 1 )}$

Let one of the two equal complementary angles be $\underline{x}$.

∴ $\textbf{ x + x = 90°}$

= > $\bold{2x = 90°}$

= > $\bold{x = \frac{90°}{2} = 45°}$

Thus, 45° is equal to its complement.

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$\bold{Soln: 2 )}$

Let $\underline{x}$ be two equal angles to its supplement.

Therefore, $\bold{x + x = 180°}$

= > $\bold{2x = 180°}$

= > $\bold{x = \frac{180°}{2} = 90°}$

Thus, 90° is equal to its supplement.

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$\bold{\fbox{Hope\:It\:Works\:!!!}}$
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