Complementary angles are two angles that add up to 90 degrees.
In your case, the measures of the two angles are \( (4x)^\circ \) and \( (2x)^\circ \). We can set up the following equation:
\[ 4x + 2x = 90 \]
Combining like terms:
\[ 6x = 90 \]
Now, solve for \( x \):
\[ x = \frac{90}{6} = 15 \]
Now we can find the measures of the two angles:
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For \( (4x)^\circ \): \[ 4x = 4 \times 15 = 60^\circ \]
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For \( (2x)^\circ \): \[ 2x = 2 \times 15 = 30^\circ \]
Now we have:
\[ x = 15, \quad (4x)^\circ = 60^\circ, \quad \text{and } (2x)^\circ = 30^\circ \]
Thus, the final answers are:
- \( x = 15 \)
- \( (4x)^\circ = 60^\circ \)
- \( (2x)^\circ = 30^\circ \)