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 $180^\circ$.