Question

1. write an expression for ( mangle rst ). (overrightarrow{sq}) bisects ( angle tsr ) ( mangle rsq = 3x - 9 ) options: ( 3x - 9 ), ( 6x - 18 ), ( 6x - 9 ), ( 1.5x - 4.5 ) (with diagram of angle at s with rays st, sq, sr)

Explanation:

Step1: Recall Angle Bisector Definition

An angle bisector divides an angle into two equal parts. So, \( \overrightarrow{SQ} \) bisecting \( \angle TSR \) means \( m\angle RSQ = m\angle TSQ \).

Step2: Express \( m\angle RST \)

Since \( \angle RST = \angle RSQ + \angle TSQ \) and \( m\angle RSQ = m\angle TSQ = 3x - 9 \), we substitute:
\( m\angle RST = (3x - 9) + (3x - 9) \)
Simplify the expression:
\( m\angle RST = 3x - 9 + 3x - 9 = 6x - 18 \)

Answer:

\( 6x - 18 \) (corresponding to the option "6x - 18")