Question

Two adjacent angles on a straight line are in the ratio $5:4$. Find the measure of smallest angle.

Answer 1

The adjacent angles on a straight line are in the ratio of $5:4.$

Let the adjacent angles be $5x$ and $4x.$

Now, $5x+4x={180}^o$ ...{ Since adjacent angles on a straight line $={180}^o$}

$\Rightarrow 9x=180$

$\Rightarrow x=\frac{180}{9}$

$\Rightarrow x=20$

The adjacent angles are as follows:

$5x=5\times 20={100}^o$ & $4x=4\times 20={80}^o$.