Question

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

Explanation:

Step1: Use the triangle angle - sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \((u + 19)+8u+(u + 31)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \((u+8u + u)+(19 + 31)=180\), which gives \(10u+50 = 180\).

Step3: Solve for \(u\)

Subtract \(50\) from both sides: \(10u=180 - 50\), so \(10u=130\). Then divide both sides by \(10\): \(u=\frac{130}{10}\).

Answer:

\(u = 13\)