Chapter 2: Chapter 2

Problem 24

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The measure of the complement of a given angle is four times the measure of the angle. Find the measure of the given angle.

Short Answer

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The measure of the given angle is 18 degrees.

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Step by step solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Knowing what Complementary Angles Are

Firstly, it's important to know that in a pair of complementary angles, one angle is the complement of the other, which simply means that the two angles add up to 90 degrees.

Step 2: Setting Up the Equation

According to the given exercise, we know that the complement of the angle is four times the measure of the angle itself. If we call the measure of the angle \(x\), then the complement is \(4x\). From what we know about complementary angles, we have: \(x + 4x = 90\)

Step 3: Simplifying the Equation

Now, let's simplify this equation. Combining like terms, we get: \(5x = 90\)

Step 4: Solving the Equation

To get \(x\) by itself, we need to divide both sides of the equation by 5: \(x = \frac{90}{5}\)

Step 5: Calculating the Angle Measure

Doing the division, we find: \(x = 18\) So, the measure of the given angle is 18 degrees. It's always a good idea to double-check your work, so you can do so by substititing \(x = 18\) back into the original equation and confirming that it yields a true statement.

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Chapter 2: Chapter 2

The measure of the complement of a given angle is four times the measure of the angle. Find the measure of the given angle.

Short Answer

Step by step solution

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Step 1: Knowing what Complementary Angles Are

Step 2: Setting Up the Equation

Step 3: Simplifying the Equation

Step 4: Solving the Equation

Step 5: Calculating the Angle Measure

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More chapters from the book ‘Geometry’

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Chapter 5

Chapter 6

Chapter 7

Chapter 8

Chapter 9

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Chapter 18

Chapter 19

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Chapter 23

Chapter 24

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Chapter 28

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Chapter 35

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Chapter 38

Chapter 39

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Chapter 42

Chapter 43

Chapter 44

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Chapter 51

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