Question

the diagram shows a triangle. the angles are 37°, ( u - 13^circ ), and ( u - 17^circ ). what is the value of ( u )? write your answer as an integer or as a decimal rounded to the nearest tenth. ( u = \boxed{}^circ )

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, \(37 + (u - 13) + (u - 17) = 180\).

Step2: Simplify the equation

Combine like terms: \(37 + u - 13 + u - 17 = 180\) → \(7 + 2u = 180\).

Step3: Solve for \(u\)

Subtract 7: \(2u = 180 - 7 = 173\). Divide by 2: \(u = \frac{173}{2} = 86.5\).

Answer:

\(86.5\)