Question

what is the value of u?

Explanation:

Step1: Use exterior - angle property

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. For the given triangle, the exterior angle is \(u + 30^{\circ}\), and the two non - adjacent interior angles are \(u\) and \(u-12^{\circ}\). So, \(u + 30^{\circ}=u+(u - 12^{\circ})\).

Step2: Simplify the equation

\[

$$\begin{align*} u + 30^{\circ}&=u+u - 12^{\circ}\\ u + 30^{\circ}&=2u-12^{\circ} \end{align*}$$

\]

Step3: Solve for \(u\)

Subtract \(u\) from both sides of the equation: \(30^{\circ}=2u - u-12^{\circ}\), which simplifies to \(30^{\circ}=u - 12^{\circ}\). Then add \(12^{\circ}\) to both sides: \(u=30^{\circ}+12^{\circ}=42^{\circ}\).

Answer:

\(42^{\circ}\)