Question

Solve for the variable given that each quadrilateral is a parallelogram.

Answer 1

Let one of the missing angles be n°.

Since any two adjacent or consecutive angles of a parallelogram are supplementary, it follows that:

`\begin{gathered} n+n=180 \\ \text{ Therefore,} \\ 2n=180 \\ \text{ Divide both sides of the equation by }2 \\ n=(180)/(2)=90 \end{gathered}`

Since opposite angles of a parallelogram are congruent, it follows that:

`\begin{gathered} 3x=90\text{ and }6y=90 \\ \text{ Therefore,} \\ x=30\text{ and }y=15 \end{gathered}`

Therefore, the required values are:

x = 30 and y = 15