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Chapter 9: Problem 30

Find the measure of a supplement of each angle. $$ 54^{\circ} $$

Short Answer

Expert verified
The supplement of 54 degrees is 126 degrees.

Step by step solution

01

- Understand the concept of supplementary angles

Supplementary angles are two angles whose measures add up to 180 degrees. If one angle is known, the supplement can be found by subtracting the known angle from 180 degrees.
02

- Write down the formula for supplementary angles

The formula to find the supplement of an angle is: \[ \text{Supplement} = 180^{\circ} - \text{given angle} \]
03

- Substitute the given angle into the formula

Given angle = 54 degrees. Substitute this into the formula: \[ \text{Supplement} = 180^{\circ} - 54^{\circ} \]
04

- Perform the calculation

Subtract 54 degrees from 180 degrees: \[ 180^{\circ} - 54^{\circ} = 126^{\circ} \]

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Key Concepts

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

Understanding Angle Measurement
Angles are a fundamental part of geometry. They are measured in degrees, which helps us quantify how 'open' or 'closed' an angle is. A full circle is 360 degrees, so an angle that forms a straight line is 180 degrees. To put it simply, if an angle spreads out or bends more, it has more degrees.
When you measure angles, you start from a baseline and count the degrees up to where the angle ends. This is important when you're trying to figure out how angles relate to each other, especially for tasks like finding supplementary angles.
Remember:
  • An angle of less than 90 degrees is called an acute angle.
  • An angle exactly 90 degrees is a right angle.
  • An angle between 90 and 180 degrees is an obtuse angle.
  • An angle exactly 180 degrees is a straight angle.
Calculating with Degree Subtraction
When working with angles, you often need to subtract degrees to find the measurement of another angle. In our example, to find the supplement of an angle like 54 degrees, you need to subtract it from 180 degrees.
Here's a step-by-step explanation:
  • Write down the total amount of degrees in a straight angle: 180 degrees.
  • Next, subtract the given angle: 54 degrees.
  • Perform the subtraction: \[180^{\rightarrow} - 54^{\rightarrow} = 126^{\rightarrow} \]
  • The result is the supplementary angle: 126 degrees.

This process of degree subtraction is a basic but crucial skill in geometry. It helps you determine the necessary degrees to complement the given angle to form a straight line.
Importance of Basic Mathematics
Understanding basic mathematical concepts is essential for tackling geometry problems. Knowing how to add, subtract, multiply, and divide numbers helps you solve more complex problems.
In the case of finding supplementary angles, being comfortable with subtraction is key. Make sure you are familiar with the arithmetic operations as they are the building blocks of advanced concepts.
Some tips to review basic mathematics:
  • Practice simple addition and subtraction regularly.
  • Use educational tools or apps designed to strengthen basic math skills.
  • Watch tutorial videos that explain fundamental arithmetic concepts.

The more comfortable you are with basic mathematics, the easier it will be to understand and solve geometry problems.

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