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:

`(\angle A)/(\angle B)=(5)/(13)\ldots(2)`

From equation (2):

`\angle A=(5\angle B)/(13)\ldots(3)`

Now, using (3) in (1):

`\begin{gathered} (5\angle B)/(13)+\angle B=90\degree \\ (18\angle B)/(13)=90\degree \\ \angle B=(90\degree\cdot13)/(18) \\ \Rightarrow\angle B=65\degree \end{gathered}`

Finally, using this result on (3):

`\begin{gathered} \angle A=(5\cdot65\degree)/(13) \\ \therefore\angle A=25\degree \end{gathered}`