Question

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

Explanation:

Step1: Use the triangle - angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \((4u + 49)+9u+40=180\).

Step2: Combine like terms

Combine the \(u\) terms and the constant terms: \(4u+9u+49 + 40=180\), which simplifies to \(13u+89 = 180\).

Step3: Isolate the variable \(u\)

Subtract \(89\) from both sides of the equation: \(13u=180 - 89\). Then \(13u=91\).
Divide both sides by \(13\): \(u=\frac{91}{13}\).

Answer:

\(u = 7\)