Question

find the m\angle cvu.
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$$\begin{array}{r}x + 13 + 63 = 3x\\\\-13 - 13\\\\\\hline x + 50 = 3x\\\\-x\\end{array}$$

Explanation:

Step1: Use the exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(3x=(x + 13)+63\).

Step2: Simplify the equation

Simplify the right - hand side of the equation: \(3x=x+76\).

Step3: Solve for \(x\)

Subtract \(x\) from both sides: \(3x−x=x + 76−x\), which gives \(2x=76\). Then divide both sides by 2: \(x = 38\).

Step4: Find \(m\angle CVU\)

Since \(m\angle CVU = 3x\), substitute \(x = 38\) into the expression. So \(m\angle CVU=3\times38=114^{\circ}\).

Answer:

\(114^{\circ}\)