Question

the measure of \\( \angle rst \\) can be represented by the expression \\( (6x + 12) ^ { \circ } \\).
what is \\( m \angle rst \\) in degrees?
\\( 78 ^ { \circ } \\)
\\( 84 ^ { \circ } \\)
\\( 120 ^ { \circ } \\)
\\( 156 ^ { \circ } \\)

Explanation:

Step1: Set up the equation

Since \( \angle RSU = 78^{\circ}\) and \( \angle TSU=(3x - 12)^{\circ}\), and \( \angle RST=(6x + 12)^{\circ}\), and \( \angle RST=\angle RSU+\angle TSU\).
So \(6x + 12=78+(3x - 12)\).

Step2: Solve the equation for \(x\)

$$
LATEXBLOCK0
$$

Step3: Find \(m\angle RST\)

Substitute \(x = 18\) into \(6x + 12\).
\(m\angle RST=6\times18+12=108 + 12=120^{\circ}\)

Answer:

\(120^{\circ}\) (the third option)