Question
What is the measure of the complement of the supplement of a \( 142^{\circ} \) angle? The measure is \( \square^{\circ} \). (Simplify your answer.)
Ask by Mann Gibson. in the United States
Feb 22,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The measure is \( 52^{\circ} \).
Solution
Step 1: Find the supplement of the 142° angle.
Supplement = 180° − 142° = 38°.
Step 2: Find the complement of the supplement.
Complement = 90° − 38° = 52°.
Thus, the measure of the complement of the supplement is 52°.
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Simplify this solution Bonus Knowledge
To find the measure of the complement of the supplement of a \( 142^{\circ} \) angle, we first need to determine the supplement of \( 142^{\circ} \). The supplement is calculated as: \[ 180^{\circ} - 142^{\circ} = 38^{\circ} \] Next, we find the complement of \( 38^{\circ} \): \[ 90^{\circ} - 38^{\circ} = 52^{\circ} \] Therefore, the measure of the complement of the supplement of a \( 142^{\circ} \) angle is \( 52^{\circ} \).
