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:

$\begin{gathered} QT=RS \\ 4x=12 \\ x=\frac{12}{4} \\ x=3 \end{gathered}$

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

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