Complementary angles are angles that sum up to \(90^\circ\).
Given the angles \(4x\) and \(2x\), we can set up the equation:
\[ 4x + 2x = 90 \]
Combining like terms:
\[ 6x = 90 \]
To solve for \(x\), divide both sides by 6:
\[ x = \frac{90}{6} = 15 \]
Now that we have the value of \(x\), we can find the measures of the angles:
- For the angle \(4x\):
\[ 4x = 4 \times 15 = 60^\circ \]
- For the angle \(2x\):
\[ 2x = 2 \times 15 = 30^\circ \]
Thus, we have:
- \(x = 15\)
- \(4x = 60^\circ\)
- \(2x = 30^\circ\)
In summary:
- \(x = 15\)
- \(4x = 60^\circ\)
- \(2x = 30^\circ\)