Question

1. find x if st=34.
2. find m∠qsr if m∠qst=85°.

Explanation:

Question 4

Step1: Analyze the segment addition

The length of \( ST \) is the sum of \( SR \) and \( RT \). So \( ST=(10 + x)+x \).

Step2: Substitute \( ST = 34 \) and solve

Substitute \( ST = 34 \) into the equation: \( 34=10 + x+x \).
Simplify the right - hand side: \( 34=10 + 2x \).
Subtract 10 from both sides: \( 34-10=2x \), so \( 24 = 2x \).
Divide both sides by 2: \( x=\frac{24}{2}=12 \).

Step1: Analyze the angle addition

We know that \( m\angle QST=m\angle QSR + m\angle RST \). We are given that \( m\angle QST = 85^{\circ} \) and \( m\angle RST=27^{\circ} \).

Step2: Solve for \( m\angle QSR \)

Substitute the known values into the angle - addition formula: \( m\angle QSR=m\angle QST - m\angle RST \).
So \( m\angle QSR = 85^{\circ}-27^{\circ}=58^{\circ} \).

Answer:

\( x = 12 \)

Question 5