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

Insufficient data

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Yes,

30^{\circ}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Yes,

45^{\circ}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No, there exists no such pair of angles.

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C Yes, $45^{\circ}$
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 $45^{\circ}$ .

Suggest Corrections

Similar questions

Sunita knows that the sum of complementary angles is equal to $90^{\circ}$ . She thinks that there can be a pair of complementary angles such that both of them are equal. Is she correct? If yes, then find such pair of angles.

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

Q. Angles x and y form a pair of complementary angles. Can x or y be an obtuse angle? Answer in Yes/No.

Q. In a pair of complementary angles, if one angle is decreased then other angle must so that both the angles still remains complementary.

Draw the pairs of angles as described below.If that is not possible, say why.

(i) Complementary angles that are not adjacent.

(ii) Angles in a linear pair which are not supplementary.

(iii) Complementary angles that do not form a linear pair.

(iv) Adjacent angles which are not in a linear pair.

(v) Angles which are neither complementary nor adjacent.

(vi) Angles in a linear pair which are complementary.

Join BYJU'S Learning Program

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

The correct option is C Yes, 45∘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∘.