Question

determine the value of x for which r parallels s. then find the measure of angle 1 and the measure of angle 2measure angle 1= 50-2xmeasure angle 2= 110-42xthe value for which r parallels s is ......... measure angle 1= ........measure angle 2=.......

Answer 1

According to the picture, angles 1 and 2 have the same measure because they are corresponding angles. Make equal both expressions for 1 and 2 and find x.

`\begin{gathered} 50-2x=110-42x \\ 42x-2x=110-50 \\ 40x=60 \\ x=(60)/(40) \\ x=(3)/(2) \end{gathered}`

x is 3/2. Replace this value in both expression to find the measure of each angle.

`\begin{gathered} \measuredangle1=50-2x \\ \measuredangle1=50-2((3)/(2)) \\ \measuredangle1=50-3 \\ \measuredangle1=47 \\ \measuredangle2=110-42x \\ \measuredangle2=110-42((3)/(2)) \\ \measuredangle2=110-63 \\ \measuredangle2=47 \end{gathered}`

The measure of these angles is 47°