Data:
l and m are parallel lines
QR and ST are perpendicular in R
Angle 1 is 63°
The angle formed by perpendicular lines is a right angle (90°)
Angles 1 and 3 are alternate angles: angles that occur on opposite sides of a transversal line that is crossing two parallel.
Alternate angles are congruent, have the same measure.
[tex]\begin{gathered} m\angle1=m\angle3 \\ \\ m\angle3=63 \end{gathered}[/tex]
The sum of the interior angles of a triangle is always 180°. In triangle QRT:
[tex]\begin{gathered} m\angle2+m\angle3+90=180 \\ \\ m\angle2+63+90=180 \\ \\ m\angle2+153=180 \end{gathered}[/tex]
Use the equation above to find the measure of angle 2:
[tex]\begin{gathered} \text{Subtract 153 in both sides of the equation:} \\ m\angle2+153-153=180-153 \\ \\ m\angle2=27 \end{gathered}[/tex]Then, the measure of angle 2 is 27°
