Question

a)If two complementary angles are in the ratio 13:5, find them.​

Answer 1

Complementary angles are those angles which give a sum of 90°

Here the ratio of angles is given to be 13:5

Let the angles be 13x and 5x

Therefore, 13x + 5x = 90

                          18x = 90

                              x= 5

So, putting the value of x

13x = 13 × 5

     = 65

5x = 5 × 5

     =25

So, the angles will be 65° and 25°

Answer 2

To Find :-

- Those complementary angles.

Solution :-

Put $\mathbf{x}$ in the ratio

Angles are

$- 13 x - 5 x$

As we know that

- Sum of two complementary angles is $90^{\circ}$

According to question :-

$\begin{array}{l}\Rightarrow 13 x+5 x=90^{\circ} \\\Rightarrow 18 x=90^{\circ} \\\Rightarrow x=90 / 18 \\\Rightarrow x=5\end{array}$

Now

$- 13 x=13 \times 5=65^{\circ} - 5 x=5 \times 5=25^{\circ}$

Hence, the two complementary angles are $} 65^{\circ} \text { and } 25^{\circ} \text { respectively. }}$