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Chapter 1: Problem 31

Find the supplement of each angle in Exercises \(31-34\) $$74^{\circ}$$ (GRAPH CANT COPY)

Short Answer

Expert verified
The supplement of 74 degrees is 106 degrees.

Step by step solution

01

Understand the Concept of Supplementary Angles

Two angles are supplementary if the sum of their measures is 180 degrees. This means if one angle is known, the other angle can be found by subtracting the given angle from 180 degrees.
02

Identify the Given Angle

The given angle measure in this problem is 74 degrees.
03

Calculate the Supplement

To find the supplement of the given angle, subtract the given angle measure from 180 degrees:\[ 180^{\text{掳}} - 74^{\text{掳}} \]
04

Perform the Subtraction

Subtract 74 from 180:\[ 180^{\text{掳}} - 74^{\text{掳}} = 106^{\text{掳}} \]

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Key Concepts

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

Understanding Angle Measurement
Angle measurement is a crucial topic in geometry. Angles are measured in degrees, which is a unit representing 1/360th of a complete circle. For example, a right angle is 90 degrees, and a straight angle is 180 degrees. Various tools, like protractors, help measure and draw angles accurately. When working with angles, it鈥檚 important to express them using the degree symbol (掳). Knowing how to measure and identify angles helps in understanding more complex geometric concepts.
The Role of Subtraction in Finding Supplementary Angles
Subtraction plays a key role in determining the measures of supplementary angles. To find the supplement of a given angle, you need to subtract the known angle from 180 degrees. For instance, if you know one angle is \(X\) degrees and you need to find its supplement, the formula is : \[ 180^{\text{掳}} - X^{\text{掳}} \] Let's apply this with the given exercise: Suppose we have an angle of 74掳: and its supplement can be found by: \[ 180^{\text{掳}} - 74^{\text{掳}} = 106^{\text{掳}} \] This simple subtraction shows that the two angles together will always sum up to 180掳, which defines them as supplementary.
Basics of Geometry: Supplementary Angles
Geometry is the study of shapes, sizes, and the properties of space. One fundamental concept is supplementary angles. These angles are two angles whose measures add up to 180 degrees. For example:
  • If you have one angle that measures 60 degrees, its supplementary angle will measure 120 degrees.
  • If an angle measures 90 degrees, then the supplementary angle will also measure 90 degrees since 90 + 90 = 180 degrees.
Understanding supplementary angles is essential for solving many geometric problems. Working with supplementary angles frequently involves identifying a given angle and using the rule that their sum is always 180 degrees. This concept serves as a cornerstone for more advanced geometric and trigonometric studies.

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