Give the measures of the complement and the supplement of an angle measuring 35° .

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Recall the definitions: The complement of an angle is what, when added to the angle, equals 90°, and the supplement of an angle is what, when added to the angle, equals 180°.

To find the complement of the given angle (35°), set up the equation: \(\text{complement} + 35^\circ = 90^\circ\).

Solve for the complement by subtracting 35° from 90°: \(\text{complement} = 90^\circ - 35^\circ\).

To find the supplement of the given angle (35°), set up the equation: \(\text{supplement} + 35^\circ = 180^\circ\).

Solve for the supplement by subtracting 35° from 180°: \(\text{supplement} = 180^\circ - 35^\circ\).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Complementary Angles

Complementary angles are two angles whose measures add up to 90 degrees. To find the complement of a given angle, subtract its measure from 90°. For example, the complement of a 35° angle is 90° - 35° = 55°.

Supplementary Angles

Supplementary angles are two angles whose measures add up to 180 degrees. To find the supplement of a given angle, subtract its measure from 180°. For instance, the supplement of a 35° angle is 180° - 35° = 145°.

Angle Measurement and Units

Angles are measured in degrees, representing the amount of rotation between two rays. Understanding how to manipulate and calculate with degrees is essential for solving problems involving complementary and supplementary angles.

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