Question

13.
\\(\overline{sq}\\) is an angle bisector. \\(m \angle qst = 2x\\) and \\(m \angle qsr = 3x - 10\\). what is \\(m \angle rst\\)?
\\(\bigcirc\\) 40
\\(\bigcirc\\) 10
\\(\bigcirc\\) 30
\\(\bigcirc\\) 20

Explanation:

Step1: Use angle bisector property

Since \( \overline{SQ} \) is an angle bisector, \( m\angle QST = m\angle QSR \). So we set up the equation:
\( 2x = 3x - 10 \)

Step2: Solve for \( x \)

Subtract \( 2x \) from both sides:
\( 0 = x - 10 \)
Add 10 to both sides:
\( x = 10 \)

Step3: Find \( m\angle QST \) and \( m\angle QSR \)

Substitute \( x = 10 \) into \( m\angle QST = 2x \):
\( m\angle QST = 2\times10 = 20 \)
Since \( \overline{SQ} \) bisects \( \angle RST \), \( m\angle RST = m\angle QST + m\angle QSR \). But \( m\angle QST = m\angle QSR = 20 \), so \( m\angle RST = 20 + 20 = 40 \)

Answer:

40