Question

what is the value of v? write your answer as an integer or as a decimal rounded to the nearest tenth. v =
(the triangle has angles: 31°, 3v - 46°, 2v - 42°)

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, \(31 + (3v - 46) + (2v - 42) = 180\).

Step2: Simplify the left side

Combine like terms: \(31 - 46 - 42 + 3v + 2v = 180\) → \(-57 + 5v = 180\).

Step3: Solve for \(v\)

Add 57 to both sides: \(5v = 180 + 57 = 237\). Divide by 5: \(v = \frac{237}{5} = 47.4\).

Answer:

\(47.4\)