Can there be a pair of complementary angles such that both of them are equal? If yes, find the values of those angles.

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Solution

Let the measure of each angle be x.
Since the angles are complementary, their sum will be 90°.
$\Rightarrow x + x = 90^{\circ}$
$\Rightarrow 2 x = 90^{\circ}$
$\Rightarrow x = 45^{\circ}$
$∴$ It is possible to have a pair of equal angles that are complementary and measure of each of them will be $45^{\circ}$ .

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Can there be a pair of complementary angles such that both of them are equal? If yes, find the values of those angles.

Let the measure of each angle be x. Since the angles are complementary, their sum will be 90°. ⇒x+x=90∘ ⇒2x=90∘ ⇒x=45∘ ∴ It is possible to have a pair of equal angles that are complementary and measure of each of them will be 45∘.