Problem 45 The measure of an angle is given... [FREE SOLUTION]

91影视

Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

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Chapter 8: Problem 45

The measure of an angle is given. Find the measure of the supplement. $$37.4^{\circ}$$

Short Answer

Expert verified

142.6 degrees

Step by step solution

Understand the Concept of Supplementary Angles

Supplementary angles are two angles whose measures add up to 180 degrees.

Set Up the Equation

Let the given angle be $ A $. The measure of the supplementary angle $ B $ can be found using the equation: $ A + B = 180^{\circ} $. Here, $ A = 37.4^{\circ} $.

Solve for the Supplementary Angle

Substitute $ A $ into the equation and solve for $ B $: \[ 37.4^{\circ} + B = 180^{\circ} \]Subtract $ 37.4^{\circ} $ from both sides to find $ B $:\[ B = 180^{\circ} - 37.4^{\circ} = 142.6^{\circ} \]

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Key Concepts

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

angle measurement

Understanding angle measurement is crucial for solving geometric problems. Angles are measured in degrees, indicated by the symbol $^\circ$. Degrees can range from 0 to 360, and they help us describe the size of an angle's opening.

To measure an angle, you often use tools like a protractor. However, in problems like this, you鈥檒l usually work with given measurements. Here, the given angle is measured as \37.4^{\circ}\. Knowing this, we can move on to analyze relationships between angles.

linear pair

A linear pair occurs when two adjacent angles form a straight line. These angles add up to 180 degrees because a straight line measures exactly 180 degrees. Therefore, the two angles are also known as supplementary angles. This concept of linear pairs is particularly useful:

Identifying that the sum of angles in a linear pair is 180 degrees
Using this property to find unknown angle measurements

In our given exercise, understanding the linear pair concept helps us deduce the measure of the supplementary angle when another angle is given.

basic arithmetic

Basic arithmetic skills are vital when solving geometry problems. In this problem, the arithmetic operation of subtraction is essential. Here鈥檚 how you can use it to find the supplementary angle:

First, recall the key equation for supplementary angles: \A + B = 180^{\circ}\.

Given \A = 37.4^{\circ}\,
substitute it into the equation:

\37.4^{\circ} + B = 180^{\circ}\.

To isolate \B\, subtract \37.4^{\circ}\ from both sides:

\[ 180^{\circ} - 37.4^{\circ} = 142.6^{\circ} \]

So, \B\, the measure of the supplementary angle, is \142.6^{\circ}\.

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91影视

The measure of an angle is given. Find the measure of the supplement. $$37.4^{\circ}$$

Short Answer

Step by step solution

Understand the Concept of Supplementary Angles

Set Up the Equation

Solve for the Supplementary Angle

Key Concepts

angle measurement

linear pair

basic arithmetic

One App. One Place for Learning.

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