Question

a triangle has interior angle measures of 31°, 2c − 10°, and c + 3°. what is the value of c? write your answer as an integer or as a decimal rounded to the nearest tenth. c = ☐° submit

Explanation:

Step1: Recall triangle angle sum

The sum of interior angles of a triangle is \(180^\circ\). So, we set up the equation: \(31 + (2c - 10) + (c + 3) = 180\).

Step2: Simplify the left side

Combine like terms: \(31 - 10 + 3 + 2c + c = 180\) → \(24 + 3c = 180\).

Step3: Solve for c

Subtract 24 from both sides: \(3c = 180 - 24 = 156\). Then divide by 3: \(c = \frac{156}{3} = 52\).

Answer:

\(52\)