Question

find the measure of the angle indicated. (equation required)

1. find ( mangle s ).

Explanation:

Step1: Use the exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(10 + 5x+105=25x - 5\).

Step2: Solve the equation for \(x\)

Simplify the left - hand side: \(115+5x = 25x-5\).
Subtract \(5x\) from both sides: \(115=20x - 5\).
Add \(5\) to both sides: \(120 = 20x\).
Divide both sides by \(20\): \(x = 6\).

Step3: Find \(m\angle S\)

Substitute \(x = 6\) into the expression for \(\angle S\) (\(10 + 5x\)).
\(m\angle S=10+5\times6\).
\(m\angle S=10 + 30\).

Answer:

\(m\angle S = 40^{\circ}\)