https://file.aiquickdraw.com/mathbot/file/1726157909726vrqz094w.jpg

The triangle in the image is a right triangle, as indicated by the 90° angle. The other two angles are labeled as \( 33^\circ \) and \( (5x - 13)^\circ \).

To solve for \( x \), we can use the fact that the sum of the angles in a triangle is always \( 180^\circ \). Therefore, we can write the equation:

\[
33^\circ + (5x - 13)^\circ + 90^\circ = 180^\circ
\]

Let's simplify and solve for \( x \):

\[
33 + 5x - 13 + 90 = 180
\]
\[
110 + 5x = 180
\]
\[
5x = 180 - 110
\]
\[
5x = 70
\]
\[
x = \frac{70}{5}
\]
\[
x = 14
\]

Thus, \( x = 14 \).

Would you like more details on any part of the solution? Here are 5 related questions for further practice:

1. What is the value of the unknown angle when \( x = 14 \)?
2. How would the solution change if the angle opposite the right angle were labeled differently?
3. Can you derive the formula for the sum of the angles of any triangle?
4. What are some methods for solving non-right triangles?
5. How would this problem change if the triangle were not a right triangle?

**Tip**: Always remember the rule that the sum of the angles in any triangle is 180°. This is helpful in various triangle-related problems!

The measures of the angles of a triangle are shown in the figure. Solve for x.

Learn how to solve for x in a triangle where the angles are 33°, 90°, and (5x - 13)°. This problem involves using the formula for the sum of the angles in a triangle, which is 180°, and applying basic algebra to solve for x.

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