Question

Consider parallelogram QRST below.Use the information given in the figure to find m ZR, x, and m ZROS.R.4x1275040°7S

Answer 1

The opposite angles of a parallelogram are equal, therefore:

`\begin{gathered} m\angle R=m\angle T \\ so\colon \\ m\angle R=75 \end{gathered}`

Opposite sides of a parallelogram are parallel and equal so:

`\begin{gathered} QT=RS \\ 4x=12 \\ x=(12)/(4) \\ x=3 \end{gathered}`

∠TSQ and ∠RQS are alternate interior angles, therefore:

`\begin{gathered} m\angle RQS=m\angle TSQ \\ so_{}\colon \\ m\angle RQS=40 \end{gathered}`