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The Triangle Angle Sum Theorem states that the sum of the interior angles of a triangle is always 180°.
In the first triangle with angles 45°, 45°, and a right angle of 90°, using the theorem we can verify:
45° + 45° + 90° = 180°
So, the measures of each angle of this triangle are 45°, 45°, and 90°.
Therefore, the first option is correct: 45°, 45°, 90°.