Ratio: Using angles in a triangle

To solve this problem, let's follow these steps:

• Step 1: Identify the given information; one angle is $90^\circ$, and the other two angles are in a 2:1 ratio.
• Step 2: Set up an equation using the relationship between the angles: $90^\circ + 2x + x = 180^\circ$.
• Step 3: Solve the equation for $x$.
• Step 4: Calculate the measures of the two angles.

Now, let's work through each step.
Step 1: Given a right triangle, one angle is $90^\circ$, and the other two angles are in the ratio 2:1.

Step 2: Express the other two angles in terms of $x$:
- One angle is $2x$.
- The second angle is $x$.

Step 3: Use the sum of angles in a triangle to write an equation:
$90^\circ + 2x + x = 180^\circ$.

Step 4: Simplify and solve the equation:
Combine like terms:
$90^\circ + 3x = 180^\circ$.

Subtract $90^\circ$ from both sides:
$3x = 90^\circ$.

Divide both sides by 3:
$x = 30^\circ$.

Now we can find the measures of the other angles:
The angle expressed as $x$ is $30^\circ$.
The angle expressed as $2x$ is $2 \times 30^\circ = 60^\circ$.

Therefore, the solution is that the other two angles are $60^\circ$ and $30^\circ$.