Question

the diagram shows a triangle. what is the value of u? write your answer as an integer or as a decimal rounded to the nearest tenth. u = \square° (angles in the triangle: 32°, 2u, u - 21°)

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, \(2u + (u - 21^\circ) + 32^\circ = 180^\circ\).

Step2: Simplify the equation

Combine like terms: \(2u + u - 21 + 32 = 180\) → \(3u + 11 = 180\).

Step3: Solve for \(u\)

Subtract 11: \(3u = 180 - 11 = 169\). Divide by 3: \(u = \frac{169}{3} \approx 56.3\).

Answer:

\(56.3\)