Complementary angles are two angles that add up to 90 degrees. Given the measures of the angles are \( (4x)^\circ \) and \( (2x)^\circ \), we can set up the following equation:
\[ 4x + 2x = 90 \]
Combining like terms gives:
\[ 6x = 90 \]
Now we can solve for \( x \):
\[ x = \frac{90}{6} = 15 \]
Now that we have found \( x \), we can find the measures of the two angles:
- \( (4x)^\circ = 4 \cdot 15 = 60^\circ \)
- \( (2x)^\circ = 2 \cdot 15 = 30^\circ \)
Thus, the values are:
- \( x = 15 \)
- \( (4x)^\circ = 60^\circ \)
- \( (2x)^\circ = 30^\circ \)
Final values:
\[ x = 15, \quad (4x)^\circ = 60^\circ, \quad (2x)^\circ = 30^\circ \]
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