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# Class 9 SELINA Solutions Maths Chapter 25 - Complementary Angles

## Complementary Angles Exercise Ex. 25

### Solution 1(a)

Correct option: (iii) 45o

sin A = cos A

Now,

### Solution 1(b)

Correct option: (iv) A + B = 90o

If sin A = cos B (A ≠ B), then A and B are complementary angles.

A + B = 90o

OR

### Solution 1(c)

Correct option: (i) 1

If A + B = 90o, then

cos A = sin B

cot A = tan B

### Solution 1(d)

Correct option: (ii) 2

### Solution 1(e)

Correct option: (iv)

### Solution 4(i)

L.H.S.

= tan 10° tan 15° tan 75° tan 80°

= tan (90° - 80°) tan (90° - 75°) tan 75° tan 80°

= cot 80° cot 75 ° tan 75° tan 80°

= (cot 80° tan 80°)(cot 75° tan 75°)

= (1)(1)

= 1

= R.H.S.

### Solution 6

(i) We know that for a triangle ABC

A + B + C = 180°

(ii) We know that for a triangle ABC

A + B + C = 180°

B + C = 180° - A

(i)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix)

## Complementary Angles Exercise Test Yourself

Now,

So,

### Solution 13

*Back answer is A = 14o. This is possible if the question is  as follows: