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Chapter 8: Problem 40

The measure of an angle is given. Find the measure of the complement. $$1^{\circ}$$

Short Answer

Expert verified
89^{\,\circ}

Step by step solution

01

Understand the Concept of Complementary Angles

Complementary angles are two angles whose measurements add up to 90 degrees.
02

Identify the Given Angle

The given angle is \(1^{\,\circ}\).
03

Set Up the Equation

Let \(x\) be the measure of the complement of the given angle. The equation will be: \(x + 1^{\,\circ} = 90^{\,\circ}\).
04

Solve the Equation

Isolate \(x\) by subtracting \(1^{\,\circ}\) from both sides: \(x = 90^{\,\circ} - 1^{\,\circ}\).
05

Calculate the Measure of the Complement

Perform the subtraction: \(90^{\,\circ} - 1^{\,\circ} = 89^{\,\circ}\).

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Key Concepts

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

angle measurements
In geometry, angles are a measure of the amount of turn between two straight lines that have a common end point (or vertex). Angles are usually measured in degrees, and a full circle is 360 degrees. Common measures for specific angles include:
  • Right angle: 90 degrees
  • Straight angle: 180 degrees
  • Full rotation: 360 degrees
It's important to note that angles can be measured using various tools such as protractors to ensure accurate results. Understanding the way angles work and their different measurements is crucial in solving various geometric problems.
basic algebra
Algebra is a branch of mathematics that deals with symbols and the rules for manipulating those symbols. It is a unifying thread of almost all of mathematics and includes everything from solving elementary equations to studying abstractions such as groups, rings, and fields. In our exercise, we use a simple algebraic equation to find the measure of the complementary angle. Here's a quick rundown of the steps taken:
  • Identify the given information (the angle measure, which is 1 degree).
  • Set up an equation where the sum of the angle and its complement equals 90 degrees.
  • Isolate the variable to solve for the unknown angle.
These steps are straightforward but pivotal in correctly finding the solution.
complementary angles calculation
Complementary angles are two angles that add up to 90 degrees. This concept is essential in various geometric problems and calculations. Let's see how to calculate the complementary angle step-by-step based on our given exercise:
  • Step 1: Understand that complementary angles sum up to 90 degrees.
  • Step 2: Identify the given angle, which is 1 degree in this case.
  • Step 3: Set up the equation: Let x be the measure of the complement. Then, x + 1 degree = 90 degrees.
  • Step 4: Solve the equation by isolating x: x = 90 degrees - 1 degree.
  • Step 5: Perform the calculation: 90 degrees - 1 degree = 89 degrees.
Thus, the measure of the complement of a 1-degree angle is 89 degrees. This simple calculation shows how understanding basic algebra and angle measurements leads to finding complementary angles effectively.

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Most popular questions from this chapter

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