Question

find m∠s. 140°

Explanation:

Step1: Use exterior - angle property

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. In \(\triangle RST\), the exterior angle at \(R\) is \(140^{\circ}\), and the two non - adjacent interior angles are \((3x + 4)^{\circ}\) and \((8x+4)^{\circ}\). So, \(140=(3x + 4)+(8x + 4)\).

Step2: Simplify the equation

Combine like terms: \(140 = 3x+8x + 4 + 4\), which gives \(140=11x + 8\).

Step3: Solve for \(x\)

Subtract 8 from both sides: \(140−8 = 11x\), so \(132 = 11x\). Then divide both sides by 11: \(x=\frac{132}{11}=12\).

Step4: Find \(m\angle S\)

We know that \(m\angle S=(3x + 4)^{\circ}\). Substitute \(x = 12\) into the expression: \(m\angle S=3\times12 + 4=36 + 4=40^{\circ}\).

Answer:

\(40^{\circ}\)