Let the measure of the angle be \( x \) degrees. The measure of its supplementary angle is then \( 180 - x \) degrees.
According to the problem, the measure of the angle is forty-four times the measure of its supplementary angle. This can be expressed with the equation: \[ x = 44(180 - x) \]
Now, let's solve this equation step-by-step.
First, distribute the 44 on the right side: \[ x = 7920 - 44x \]
Next, add \( 44x \) to both sides to combine like terms: \[ x + 44x = 7920 \] \[ 45x = 7920 \]
Now, divide both sides by 45 to solve for \( x \): \[ x = \frac{7920}{45} \] \[ x = 176 \]
Now that we have \( x \), we can find the measure of the supplementary angle: \[ 180 - x = 180 - 176 = 4 \]
Thus, the measures of the angles are:
- The first angle: \( 176^\circ \)
- The supplementary angle: \( 4^\circ \)
To summarize, the measures of the angles are \( 176^\circ \) and \( 4^\circ \).
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