Question

A and«B are complementary angles. The ratio of

Answer 1

∠A and ∠B are complementary angles:

$\angle A+\angle B=90\degree\ldots(1)$

The ratio of ∠A to ∠B is 5 : 13:

$\frac{\angle A}{\angle B}=\frac{5}{13}\ldots(2)$

From equation (2):

$\angle A=\frac{5\angle B}{13}\ldots(3)$

Now, using (3) in (1):

$\begin{gathered} \frac{5\angle B}{13}+\angle B=90\degree \\ \frac{18\angle B}{13}=90\degree \\ \angle B=\frac{90\degree\cdot13}{18} \\ \Rightarrow\angle B=65\degree \end{gathered}$

Finally, using this result on (3):

$\begin{gathered} \angle A=\frac{5\cdot65\degree}{13} \\ \therefore\angle A=25\degree \end{gathered}$