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The measure of an angle is \( 132^{\circ} \). What is the measure of its supplementary angle?

Ask by Pope Li. in the United States
Mar 20,2025

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Answer

The supplementary angle is \(48^{\circ}\).

Solution

1. Two angles are supplementary if their measures add up to \(180^{\circ}\). 2. Let \( x \) be the measure of the supplementary angle. Then, we have: \[ 132^{\circ} + x = 180^{\circ} \] 3. To solve for \( x \), subtract \(132^{\circ}\) from both sides: \[ x = 180^{\circ} - 132^{\circ} \] 4. Calculate the difference: \[ x = 48^{\circ} \] Thus, the measure of the supplementary angle is \(48^{\circ}\).

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Beyond the Answer

To find the measure of the supplementary angle, you simply subtract the given angle from \( 180^{\circ} \). So, \( 180^{\circ} - 132^{\circ} = 48^{\circ} \). Therefore, the supplementary angle measures \( 48^{\circ} \). Did you know that the concept of supplementary angles dates back to ancient civilizations? The Greeks were particularly interested in geometry and used angles in their architectural designs, making sure to include considerations for both supplementary and complementary angles in their work! You can put this knowledge to practical use by applying it in real-world situations like interior design or architecture! Understanding how angles work helps create harmonious and aesthetically pleasing spaces, whether designing a room or constructing a building, ensuring the angles fit perfectly together for the desired effect.

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