Question

find the value of x
find the m\\( \angle u v t \\)

Explanation:

Step1: Apply 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

$$
LATEXBLOCK0
$$

Step3: Solve for \(x\)

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

Step4: Find \(m\angle UVT\)

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

Answer:

The value of \(x\) is \(38\) and \(m\angle UVT\) is \(114^{\circ}\).