Question

Question 2
Find those pairs of angles that are complementary to each other and also of same measure.

Answer 1

Complementary angles are those angles which add up to a right angle.

Let x, y be two angles.

Given x, y are complementary angles

⇒ x + y = 90°

Given, x, y are of same measure

⇒x = y

⇒ x - y = 0

Solving (1) & (2)

⇒ x + y = 90

⇒ x - y = 0

Adding both of them gives,

⇒ 2x = 90

⇒ x = 90 ÷ 2

⇒ x = 45°

Subtracting both of them gives,

⇒ 2y = 90

⇒ y = 90 ÷ 2

⇒ y = 45°

Therefore, The angles are 45° & 45°

Answer 2

Complementary angles are those pair of angles whose magnitude give a sum total of 90°.

Let the first angle be = a

And the second angle = b.

According to question ,

a+b = 90°

=> a+a = 90° (a=b)

=> 2a = 90°

Angle a = 45°

Angle b = 45° .

Required pair = 45° and 45°