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.
[tex]\begin{gathered} 50-2x=110-42x \\ 42x-2x=110-50 \\ 40x=60 \\ x=\frac{60}{40} \\ x=\frac{3}{2} \end{gathered}[/tex]
x is 3/2. Replace this value in both expression to find the measure of each angle.
[tex]\begin{gathered} \measuredangle1=50-2x \\ \measuredangle1=50-2(\frac{3}{2}) \\ \measuredangle1=50-3 \\ \measuredangle1=47 \\ \measuredangle2=110-42x \\ \measuredangle2=110-42(\frac{3}{2}) \\ \measuredangle2=110-63 \\ \measuredangle2=47 \end{gathered}[/tex]
The measure of these angles is 47°
