Question

2.c)in the diagram below, 4 m and ORIST at R. 5 $ 0 If m_1 = 63, find m_2.

Answer 1

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.

$\begin{gathered} m\angle1=m\angle3 \\ \\ m\angle3=63 \end{gathered}$

The sum of the interior angles of a triangle is always 180°. In triangle QRT:

$\begin{gathered} m\angle2+m\angle3+90=180 \\ \\ m\angle2+63+90=180 \\ \\ m\angle2+153=180 \end{gathered}$

Use the equation above to find the measure of angle 2:

$\begin{gathered} \text{Subtract 153 in both sides of the equation:} \\ m\angle2+153-153=180-153 \\ \\ m\angle2=27 \end{gathered}$Then, the measure of angle 2 is 27°