Question

Two adjacent angles of a parallelogram are in the ratio 2 : 3. Find the measure of each of its angles.

Answer 1

$\mathrm{Let}\mathrm{the}\mathrm{two}\mathrm{adjacent}\mathrm{angles}\mathrm{of}\mathrm{the}\mathrm{parallelogram}\mathrm{b}\mathrm{e}\left(2x\right)°\mathrm{and}\left(3x\right)°.$
Sum of any two adjacent angles of a parallelogram is ${180}^{\circ }$.

$$\begin{gathered} \therefore 2x+3x=180 \\ \Rightarrow 5x=180 \\ \Rightarrow x=36 \end{gathered}$$

$$\begin{gathered} \left(2x\right)°=(2\times 36)°={72}^{\circ } \\ \left(3x\right)°=(3\times 36)°={108}^{\circ } \end{gathered}$$

Measures of the angles are ${72}^{\circ }and{108}^{\circ }$.