Complementary angles are two angles whose measures add up to 90 degrees. Given that the angles are \( (2x)^\circ \) and \( (3x)^\circ \), we can write the equation:
\[ 2x + 3x = 90 \]
Now, combine like terms:
\[ 5x = 90 \]
Next, solve for \( x \) by dividing both sides by 5:
\[ x = \frac{90}{5} = 18 \]
Now that we have the value of \( x \), we can find the measures of the two angles.
- For the first angle \( (2x)^\circ \):
\[ 2x = 2 \times 18 = 36^\circ \]
- For the second angle \( (3x)^\circ \):
\[ 3x = 3 \times 18 = 54^\circ \]
Thus, the values are:
- \( x = 18 \)
- \( (2x)^\circ = 36^\circ \)
- \( (3x)^\circ = 54^\circ \)
So, in summary:
\[ x = 18, \quad (2x)^\circ = 36^\circ, \quad (3x)^\circ = 54^\circ \]
1 answer