Question

a triangle has interior angle measures of 4v, 2v, and v + 14°. what is the value of v?
write your answer as an integer or as a decimal rounded to the nearest tenth.
v =
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Explanation:

Step1: Use the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(4v + 2v+(v + 14)=180\).

Step2: Combine like terms

Combine the \(v\) terms: \((4v+2v + v)+14 = 180\), which simplifies to \(7v+14 = 180\).

Step3: Isolate the variable term

Subtract \(14\) from both sides: \(7v+14 - 14=180 - 14\), so \(7v=166\).

Step4: Solve for \(v\)

Divide both sides by \(7\): \(v=\frac{166}{7}\approx23.7\).

Answer:

\(23.7\)