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Two supplementary angles are in the ratio $3: 2$. Find the angles.

Solution

Let the measures of the given angles be $(3 x)^{\circ}$ and $(2 x)^{\circ}$ respectively.

Since the given angles are supplementary, we have

$$3 x+2 x=180 \Rightarrow 5 x=180 \Rightarrow x=36$$

$\therefore$ the measures of the given angles are $(3 \times 36)^{\circ}$ and $(2 \times 36)^{\circ}$, i.e, $108^{\circ}$ and $72^{\circ}$ respectively.

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