In a right triangle, the sum of the angles is always 180 degrees. Since triangle B-C-A is right-angled at C, one of the angles is 90 degrees. Thus, we can establish the following relationship between the angles:
\[ \text{Angle A} + \text{Angle B} + \text{Angle C} = 180^\circ \]
Given that angle A is \( x \) degrees, angle B is \( 2x \) degrees, and angle C is \( 90^\circ \), we can substitute these values into the equation:
\[ x + 2x + 90^\circ = 180^\circ \]
Now, combine the \( x \) terms:
\[ 3x + 90^\circ = 180^\circ \]
Next, we will isolate \( 3x \) by subtracting \( 90^\circ \) from both sides:
\[ 3x = 180^\circ - 90^\circ \] \[ 3x = 90^\circ \]
Now, divide both sides by 3 to solve for \( x \):
\[ x = \frac{90^\circ}{3} \] \[ x = 30^\circ \]
Therefore, the solution for \( x \) is:
\[ \boxed{30^\circ} \]
1 answer