Bowers Bowen
08/31/2023 · Senior High School

10 points Suppose \( \angle A \) and \( \angle B \) are complementary. Which of the following is correct? None of these \( m \angle A+m \angle B=90 \) If these If \( m \angle A=72^{\circ} \), then \( m \angle B=37^{\circ} \), then \( m \angle B \neq 75^{\circ} \)

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To determine which statement is correct regarding complementary angles, we need to recall the definition of complementary angles: two angles are complementary if the sum of their measures is \(90^\circ\). 1. **None of these**: This option is not valid unless all other options are incorrect. 2. **\( m \angle A + m \angle B = 90 \)**: This statement is correct because it directly reflects the definition of complementary angles. 3. **If \( m \angle A = 72^\circ \), then \( m \angle B = 37^\circ \)**: This statement is incorrect. If \( m \angle A = 72^\circ \), then \( m \angle B \) should be \( 90^\circ - 72^\circ = 18^\circ\), not \(37^\circ\). 4. **Then \( m \angle B \neq 75^\circ \)**: This statement is true because if \( m \angle A = 72^\circ \), then \( m \angle B \) cannot be \(75^\circ\) as it would not satisfy the complementary condition. Given these evaluations, the correct answer is: **\( m \angle A + m \angle B = 90 \)**.

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\( m \angle A + m \angle B = 90 \)
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