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This is a right triangle with angles labeled as \( a^\circ \), \( 2a^\circ \), and \( 90^\circ \). Since the sum of the angles in any triangle is always \( 180^\circ \), we can set up the following equation:

\[
a^\circ + 2a^\circ + 90^\circ = 180^\circ
\]

Now, let's solve for \( a \):

\[
3a + 90 = 180
\]
\[
3a = 180 - 90
\]
\[
3a = 90
\]
\[
a = \frac{90}{3} = 30
\]

Thus, \( a^\circ = 30^\circ \). This makes the other angle \( 2a^\circ = 60^\circ \).

So, the angles of the triangle are:

- \( a^\circ = 30^\circ \)
- \( 2a^\circ = 60^\circ \)
- \( 90^\circ \) (right angle)

Would you like more details on how this relates to trigonometric functions or geometric properties?

Here are some follow-up questions:
1. What are the side ratios of this triangle based on its angles?
2. How does the triangle relate to special triangles (like the 30-60-90 triangle)?
3. Can we calculate the sides if given one side of the triangle?
4. How can the sine, cosine, and tangent of the angles be computed?
5. What would happen if one of the angles was changed?

**Tip:** In any triangle, the sum of interior angles is always \(180^\circ\), which is a key property used for solving unknown angles.

Find the angles of the right triangle with angles labeled a°, 2a°, and 90°.

Learn how to solve for the angles of a right triangle where the angles are labeled a°, 2a°, and 90°. This problem uses basic geometry principles such as the sum of angles in a triangle. Suitable for students in Grades 6-8.

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