How to find supplement and complement angles?

Understand the Problem

The question is asking how to determine the values of supplement and complement angles. Supplementary angles are two angles whose sum is 180 degrees, while complementary angles are two angles whose sum is 90 degrees. The approach will involve identifying one angle and then using these definitions to calculate the other angle.

Answer

If the angle is $x$, the supplementary angle is $180^\circ - x$ and the complementary angle is $90^\circ - x$.

Steps to Solve

Define the angle you know Identify the angle you are given. For example, let's call it $x$ degrees.
Calculate the supplementary angle To find the supplementary angle, use the formula: $$ \text{Supplementary Angle} = 180^\circ - x $$ This shows how to determine the angle that combines with $x$ to total 180 degrees.
Calculate the complementary angle To find the complementary angle, use the formula: $$ \text{Complementary Angle} = 90^\circ - x $$ This calculation finds the angle that combines with $x$ to total 90 degrees.
Write down both angles Once you have both calculations, articulate the results clearly, stating the values of both the supplementary and complementary angles.

If $x$ is the given angle, the supplementary angle is $180^\circ - x$ and the complementary angle is $90^\circ - x$.

More Information

Supplementary and complementary angles are fundamental concepts in geometry, often used in various applications, including trigonometry and real-world problem solving. Knowing how to find these angles is essential for working with polygons and angle relationships.

Tips

A common mistake is misinterpreting supplementary and complementary angles. Remember, supplementary angles sum to 180 degrees, while complementary angles sum to 90 degrees.
Another mistake is forgetting to subtract the given angle from 180 or 90 degrees. Always perform the subtraction to find the correct angle.

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