Question

a triangle has interior angle measures of s, s - 7°, and 2s - 10°. what is the value of s? write your answer as an integer or as a decimal rounded to the nearest tenth. s =

Explanation:

Step1: Use the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(s+(s - 7)+(2s-10)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \((s + s+2s)+(-7 - 10)=180\), which gives \(4s-17 = 180\).

Step3: Solve for \(s\)

Add \(17\) to both sides of the equation: \(4s-17 + 17=180 + 17\), so \(4s=197\). Then divide both sides by \(4\): \(s=\frac{197}{4}=49.25\).

Answer:

\(49.3\)