Question

m∠rsu = 76°. m∠rst = ____°. r s t u (7x + 8)° (3x - 2)°

Explanation:

Step1: Set up the equation

Since \(m\angle RSU=m\angle RST + m\angle TSU\), we have \(76=(7x + 8)+(3x-2)\).
Simplify the right - hand side: \(76 = 7x+8 + 3x-2=10x + 6\).

Step2: Solve for \(x\)

Subtract \(6\) from both sides: \(76-6=10x\), so \(70 = 10x\).
Divide both sides by \(10\): \(x=\frac{70}{10}=7\).

Step3: Find \(m\angle RST\)

Substitute \(x = 7\) into the expression for \(m\angle RST\) (\(7x + 8\)).
\(m\angle RST=7\times7+8=49 + 8=57\).

Answer:

\(57\)