Question

the diagram shows a triangle. what is the value of u?

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. So, \((u - 50^{\circ})+(u - 50^{\circ})+(u - 50^{\circ})=180^{\circ}\).

Step2: Simplify the left - hand side

Combine like terms: \(3(u - 50^{\circ})=180^{\circ}\).

Step3: Expand the left - hand side

Using the distributive property \(3u-150^{\circ}=180^{\circ}\).

Step4: Solve for \(u\)

Add 150° to both sides: \(3u=180^{\circ}+150^{\circ}\), so \(3u = 330^{\circ}\). Then divide both sides by 3: \(u=\frac{330^{\circ}}{3}=110^{\circ}\).

Answer:

\(110\)