Question

Type the correct answer in each box. Use numerals instead of words In the figure, lines BD and QS are parallel

Answer 1

..Given: Two parallel lines BD and QS and a transversal AT

To Determine: The measure of CRQ and CRS

Solution

From the image given, angle DCR and CRQ are alternate angles

Also angle DCR and angle CRS are each pair of the same interior angles

Please note that alternates angles are equal and each pair of same-side interior angles are supplementary

Apply the theorem above

`\begin{gathered} \angle CRQ=\angle DCR(alternate-angles) \\ \angle CRQ=77^0 \end{gathered}`

Also

`\begin{gathered} \angle DCR+\angle CRS=180^0(same-ineterior-angles) \\ 77^0+\angle CRS=180^0 \\ \angle CRS=180^0-77^0 \\ \angle CRS=103^0 \end{gathered}`

Hence:

∠CRQ = 77⁰

∠CRS = 103⁰