Question

If the ratio of measures of two adjacent angles of a parallelogram is 1 : 2, find the measures of all angles of the parallelogram.

Answer 1

Let the two adjacent angles be $x\mathrm{and}2x$.
Interior angles on the same side of the transversal are supplementary.
So,
$$\begin{gathered} x+2x=180° \\ \Rightarrow 3x=180° \\ \Rightarrow x=60° \end{gathered}$$
Thus, the adjacent angles are $60°\mathrm{and}120°$.
The opposite angles of a parallelogram are congruent.
So, the angles of the parallelogram will be $60°,120°$, $60°\mathrm{and}120°$.