Question

1. if m ∠rst = 70, m ∠qst = 2x, and m ∠qsr = 3x − 10, what is the m ∠qsr ?

16
38
32
48

Explanation:

Step1: Identify angle relationship

From the diagram, \( \angle RST = \angle QST + \angle QSR \). So, \( 70 = 2x + (3x - 10) \).

Step2: Solve for \( x \)

Simplify the equation: \( 70 = 5x - 10 \). Add 10 to both sides: \( 80 = 5x \). Divide by 5: \( x = 16 \).

Step3: Find \( m\angle QSR \)

Substitute \( x = 16 \) into \( 3x - 10 \): \( 3(16) - 10 = 48 - 10 = 38 \).

Answer:

38