Question

topic 3: classwork review for 2nd 9 - weeks
part 1 of 2
find the angle of rotation for the rotation that is the composition ( r_{n} circ r_{m} ). then, draw the image
the angle of rotation is
(simplify your answer.)

Explanation:

Step1: Recall rotation by reflections

The composition of two reflections \( r_n \circ r_m \) (first reflect over line \( m \), then over line \( n \)) is a rotation about the intersection point \( S \) of lines \( m \) and \( n \). The angle of rotation is twice the angle between the two lines.

Step2: Identify the angle between lines

From the diagram, the angle between lines \( m \) and \( n \) is \( 78^\circ \).

Step3: Calculate the rotation angle

Using the property, the angle of rotation \( \theta = 2\times78^\circ = 156^\circ \).

Answer:

\( 156^\circ \)