https://file.aiquickdraw.com/mathbot/file/172628940248528i2vqgx.jpg

The image shows a right triangle with two given angles:

1. One angle is labeled \( 21^\circ \).
2. Another angle is labeled \( 2x - 1^\circ \), next to the right angle.

In a right triangle, the sum of all angles is always \( 180^\circ \). Since one angle is \( 90^\circ \) (the right angle), the other two angles must sum to \( 90^\circ \).

Thus, we can form the equation:

\[
21^\circ + (2x - 1)^\circ = 90^\circ
\]

Now let's solve for \( x \):

\[
21 + 2x - 1 = 90
\]

Simplifying:

\[
20 + 2x = 90
\]

\[
2x = 70
\]

\[
x = 35
\]

Therefore, \( x = 35 \). The angle \( 2x - 1 \) is:

\[
2(35) - 1 = 69^\circ
\]

So the unknown angle is \( 69^\circ \).

Would you like further details on this calculation? Here are some related questions:

1. How do you verify the sum of angles in any triangle?
2. What are some common properties of right triangles?
3. Can you explain how trigonometric functions work with these angles?
4. How does solving equations like \( 2x - 1 \) apply to other geometry problems?
5. How would this problem change if it were not a right triangle?

**Tip:** Always check if the sum of angles matches 180° when solving problems in triangles.

Solve for x in the right triangle where one angle is labeled 21° and the other is labeled 2x - 1°.

Learn how to solve for x in a right triangle where one angle is 21° and the other is represented as 2x - 1°. This problem involves properties of right triangles and basic algebra, suitable for students in Grades 7-9.

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