Question

the angles are complementary and the smaller is 40 degree less than the larger

Answer 1

Given:

Two angles are complimentary.

Difference between two angles=40°

To Find:

Both the angles.

Solution:

Let one angle be x°.

Then, other angle will be (x+40)°(The difference of both the angles is 40°).

According to question, both the angles are complimentary.

That means, the sum of both the angles will be 90°.

⇒x°+(x+40)°=90°

⇒x°+x°+40°=90°

⇒2x°+40°=90°

⇒2x°=90°-40°

⇒2x°=50°

⇒x°=$\dfrac{50}{2}$°

⇒x°=25°

So, one angle is 25° and other angle is (25+40)°=65°

∴The required angles are 25° and 65°.