Question

what is the measure of angle x?
triangle stu is similar to triangle vwx.

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle STU\sim\triangle VWX\), corresponding angles are equal.

Step2: Sum of angles in a triangle

In \(\triangle STU\), we know one angle is \(16^{\circ}\) and another is \(25^{\circ}\). Using the angle - sum property of a triangle (\(\angle S+\angle T+\angle U = 180^{\circ}\)), and in \(\triangle VWX\), \(\angle X\) corresponds to \(\angle U\).
First, find \(\angle U\) in \(\triangle STU\): \(\angle U=180^{\circ}-(16^{\circ} + 25^{\circ})\)

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Answer:

\(139^{\circ}\)