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Chapter 9: Problem 32

Find the measure of a supplement of each angle. $$ 13^{\circ} $$

Short Answer

Expert verified
The supplementary angle is 167掳.

Step by step solution

01

Understand the Concept of Supplementary Angles

Supplementary angles are two angles whose measures add up to 180掳. This means if you have one angle, the supplement is what you add to it to get 180掳.
02

Set Up the Equation

Let's denote the measure of the supplement of the given angle as \(x\). According to the definition, the equation will be: \[ 13^\text{掳} + x = 180^\text{掳} \]
03

Solve for \(x\)

To find \(x\), subtract 13掳 from both sides of the equation: \[ x = 180^\text{掳} - 13^\text{掳} \]
04

Perform the Calculation

Now, perform the subtraction: \[ x = 167^\text{掳} \]
05

State the Final Answer

The supplement of an angle measuring 13掳 is 167掳.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Angle Measures
Understanding angle measures is crucial in geometry. Angles are measured in degrees (掳). There are different types of angles such as acute, obtuse, and right angles.
Supplementary angles are a specific type where two angles sum to 180掳. If you have one angle, you can always find its supplement by subtracting it from 180掳. This basic idea helps solve problems related to supplementary angles.
Basic Arithmetic
Basic arithmetic involves fundamental mathematical operations like addition, subtraction, multiplication, and division. In solving for supplementary angles, subtraction is particularly important.
For example, if one angle is given as \(13\text{掳}\), and you need to find the supplementary angle, you set up an equation based on the rule that supplementary angles add up to 180掳.
This requires simple subtraction: \[ x = 180掳 - 13掳\].
Across math problems, basic arithmetic skills help you perform quick and accurate calculations to find solutions efficiently.
Subtraction
Subtraction is a fundamental arithmetic operation. It involves taking one number away from another. In the context of angles, subtraction helps you find an unknown angle when the sum is known.
To find the measure of the supplement of an angle, subtract the given angle from 180掳. For example, for an angle of 13掳 the calculation would be \( x = 180^\text{掳} - 13^\text{掳} \), which simplifies to 167掳.
Subtraction is used widely across different areas of math, making it an essential skill to master for solving various mathematical problems.

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