In a triangle, the sum of the measures of the interior angles is always 180°. Given that one interior angle is 45°, we can determine the sum of the measures of the other two angles as follows:
\[ 180° - 45° = 135° \]
This means that the sum of the measures of the other two angles is 135°. Now, let's analyze the statements one by one:
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One of the other angles must be a right angle. - This is not necessarily true. While it's possible for one of the other angles to be a right angle (which would make the other angle 90°), it is not a requirement.
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The sum of the measures of the other two angles is 135°. - This statement is true, as we calculated.
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The other two angles must be acute angles. - This is not necessarily true. The other two angles could be acute angles, but they also could be one acute angle and one obtuse angle (e.g., 45° and 90°).
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One of the other angles must have a measure greater than 90°. - This is not necessarily true, since both angles could also be less than 90° and still sum up to 135° (e.g., 67.5° and 67.5°).
From this analysis, the only conclusion that can be drawn with certainty is:
The sum of the measures of the other two angles is 135°.
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