Question

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

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. So, $(3u + 9)+(16u-13)+32 = 180$.

Step2: Combine like - terms

First, combine the u - terms and the constant terms: $(3u+16u)+(9 - 13+32)=180$, which simplifies to $19u+( - 4 + 32)=180$, then to $19u + 28=180$.

Step3: Isolate the variable term

Subtract 28 from both sides of the equation: $19u+28 - 28=180 - 28$, resulting in $19u=152$.

Step4: Solve for u

Divide both sides by 19: $u=\frac{152}{19}$. So, $u = 8$.

Answer:

$8$