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In this triangle, we have:

1. A right angle (\(90^\circ\)).
2. An angle labeled as \(2x^\circ\).
3. Another angle labeled as \(8x^\circ\).

Since this is a right triangle, the sum of the three angles must be \(180^\circ\).

Let's set up the equation for the sum of the angles:
\[
2x + 8x + 90 = 180
\]

Simplify and solve for \(x\):
\[
10x + 90 = 180
\]
\[
10x = 90
\]
\[
x = 9
\]

Now that we know \(x = 9\), we can find the measures of the two unknown angles:
- \(2x = 2 \times 9 = 18^\circ\)
- \(8x = 8 \times 9 = 72^\circ\)

So, the angles in the triangle are:
1. \(90^\circ\) (right angle)
2. \(18^\circ\)
3. \(72^\circ\)

Would you like further details or have any questions?

Here are five related questions to expand your understanding:
1. How do we classify a triangle based on its angles?
2. What would happen to the angle measures if \(x\) had a different value?
3. Can we determine side lengths from the angles in a right triangle?
4. How can we use trigonometric ratios to find side lengths in a right triangle?
5. What are the properties of complementary and supplementary angles in triangles?

**Tip:** Remember that in any triangle, the sum of the interior angles is always \(180^\circ\).

In a right triangle, if one angle is labeled as 2x° and another as 8x°, find the values of the angles.

Learn how to find the angle measures in a right triangle with one angle labeled 2x° and another labeled 8x°. This problem involves using the triangle angle sum property and solving a simple equation. Suitable for Grades 7-9.

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