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Chapter 8: Problem 42

The measure of an angle is given. Find the measure of the supplement. $$5^{\circ}$$

Short Answer

Expert verified
The supplement is 175 degrees.

Step by step solution

01

Understand the Concept of Supplementary Angles

Two angles are called supplementary if the sum of their measures is 180 degrees.
02

Identify the Given Angle

The given angle measures 5 degrees.
03

Calculate the Supplement

To find the supplementary angle, subtract the measure of the given angle from 180 degrees: \[ \text{Supplementary Angle} = 180^\text{circ} - 5^\text{circ} \]
04

Perform the Calculation

Perform the subtraction: \[ 180^\text{circ} - 5^\text{circ} = 175^\text{circ} \]
05

Write the Answer

The measure of the supplementary angle is 175 degrees.

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Key Concepts

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

Angle Measurement
An angle is formed when two rays meet at a common endpoint called the vertex. In geometry, angles are usually measured in degrees, and this unit of measurement is denoted by the symbol \(^{\circ}\). When measuring angles, it helps to understand the different types of angles:
  • Acute angles: less than 90 degrees
  • Right angles: exactly 90 degrees
  • Obtuse angles: between 90 and 180 degrees
  • Straight angles: exactly 180 degrees
To find the measure of an angle, it is common to use a protractor, which allows for precise measurements in degrees.
Subtraction in Degrees
Subtracting angles is a straightforward process when you follow the rules of arithmetic. When you have to find the supplement of an angle, you need to subtract the given angle from 180 degrees, because supplementary angles add up to 180 degrees. For example, if you are given an angle of \(5^{\circ}\), you can find its supplement by: \[ 180^{\circ} - 5^{\circ} = 175^{\circ} \] In cases where you need to subtract angles that result in a negative measurement, this would indicate that the given angle is itself beyond its supplementary counterpart, which is not usual in basic geometric applications.
Geometry Basics
Geometry is a branch of mathematics that deals with the properties and relationships of points, lines, surfaces, and shapes. Understanding some basic principles is crucial for problem-solving:
  • Point: A location with no size or dimension.
  • Line: Extends indefinitely in both directions with no thickness.
  • Ray: A part of a line that starts at a point and extends infinitely in one direction.
  • Plane: A flat surface extending indefinitely in all directions.
One of the fundamental concepts in geometry is understanding the relationships between angles. Supplementary angles are one such relationship where two angles sum to 180 degrees. This relationship is essential in various geometric problems and real-world applications, such as constructing parallel lines, architectural designs, and even art.

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