MarjorieV702222 MarjorieV702222
  • 03-11-2022
  • Mathematics
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Consider parallelogram QRST below.Use the information given in the figure to find m ZR, x, and m ZROS.R.4x1275040°7S

Consider parallelogram QRST belowUse the information given in the figure to find m ZR x and m ZROSR4x12750407S class=

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GlennF754477 GlennF754477
  • 03-11-2022

The opposite angles of a parallelogram are equal, therefore:

[tex]\begin{gathered} m\angle R=m\angle T \\ so\colon \\ m\angle R=75 \end{gathered}[/tex]

Opposite sides of a parallelogram are parallel and equal so:

[tex]\begin{gathered} QT=RS \\ 4x=12 \\ x=\frac{12}{4} \\ x=3 \end{gathered}[/tex]

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

[tex]\begin{gathered} m\angle RQS=m\angle TSQ \\ so_{}\colon \\ m\angle RQS=40 \end{gathered}[/tex]

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