Question

what is the value of x? x =

Explanation:

Step1: Recall triangle - angle - sum property

The sum of the interior angles of a triangle is 180°. In \(\triangle VUT\), we know one angle is 59° and another is \(x - 59^{\circ}\), and the third - angle is 90° (since an angle inscribed in a semi - circle is a right angle).
So, \(59+(x - 59)+90 = 180\).

Step2: Simplify the left - hand side of the equation

\[

$$\begin{align*} 59+x - 59+90&=180\\ x+90&=180 \end{align*}$$

\]

Step3: Solve for \(x\)

Subtract 90 from both sides of the equation \(x+90 = 180\).
\(x=180 - 90\)

Answer:

90