Mathematics

# Two supplementary angles are in the ratio 4:5. Find the angles.

$80^{\circ},100^{\circ}$

##### SOLUTION
The given ratio of supplementary angles is $4:5$
Let the angles be $4x$ and $5x$
$\Rightarrow$  $4x+5x=180^o$
$\Rightarrow$  $9x=180^o$
$\Rightarrow$  $x=\dfrac{180^o}{9}$
$\Rightarrow$  $x=20^o$
$\Rightarrow$  $4x=4\times 20^o=80^o$
$\Rightarrow$  $5x=5\times 20^o=100^o$
$\therefore$  Two supplementary angles are $80^o$ and $100^o.$

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