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, \((u + 44^{\circ})+(u + 39^{\circ})+85^{\circ}=180^{\circ}\).

Step2: Combine like - terms

\(u+u + 44^{\circ}+39^{\circ}+85^{\circ}=180^{\circ}\), which simplifies to \(2u+168^{\circ}=180^{\circ}\).

Step3: Isolate the variable \(u\)

Subtract \(168^{\circ}\) from both sides: \(2u=180^{\circ}-168^{\circ}\), so \(2u = 12^{\circ}\). Then divide both sides by 2: \(u=\frac{12^{\circ}}{2}=6^{\circ}\).

Answer:

\(6\)