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Chapter 8: Problem 43

The measure of an angle is given. Find the measure of the supplement. $$127^{\circ}$$

Short Answer

Expert verified
The supplement of a \(127^{\circ}\) angle is \(53^{\circ}\).

Step by step solution

01

- Understand the definition 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 given angle from 180 degrees.
02

- Set up the equation

Let the measure of the given angle be denoted as \(x\). In this case, \(x = 127^{\circ}\).
03

- Calculate the supplement

The supplement of an angle is calculated as \(180^{\circ} - x\). So, substitute \(x = 127^{\circ}\) into the equation: \(180^{\circ} - 127^{\circ} = 53^{\circ}\).
04

- Write the final answer

The measure of the supplement is \(53^{\circ}\).

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Key Concepts

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

Angle Measures
Understanding angle measures is essential before diving into supplementary angles. Angles are formed when two rays share a common endpoint, known as the vertex. The measure of an angle is usually given in degrees. In a full circle, there are 360 degrees. This circle can be divided into smaller sections, such as:
  • A right angle, which measures 90 degrees and looks like the corner of a square.
  • An acute angle, which is smaller than 90 degrees.
  • An obtuse angle, which is larger than 90 degrees but less than 180 degrees.
  • A straight angle, which measures exactly 180 degrees and looks like a straight line.
The unit of measurement for angles is degrees, denoted by the symbol \(^\text{circ} \).
Supplement Calculation
Supplementary angles are two angles that add up to 180 degrees. This is a crucial concept for solving problems related to angle supplements.
Here's a step-by-step guide:
  • First, identify the given angle measure. In our exercise, the given value is 127 degrees.
  • Use the definition of supplementary angles to set up your equation. This step involves subtracting the given angle from 180 degrees: \( x_{\text{supplement}} = 180^\text{circ} - x \)
  • Substitute the value of the given angle into the equation. For our example, it is: \( 180^\text{circ} - 127^\text{circ} \)
  • Calculate the result to find the measure of the supplement: \[ 180^\text{circ} - 127^\text{circ} = 53^\text{circ} \]

These steps help you methodically identify and calculate the measures required when dealing with supplementary angles.
Basic Arithmetic
Basic arithmetic skills are important for solving problems like calculating the supplement of an angle. The primary operations are addition, subtraction, multiplication, and division. For our specific problem:
  • Subtraction: When we calculate the supplement of an angle, we subtract the given angle from 180 degrees. For example, subtracting 127 from 180 to find the unknown supplement.

Let's lay out the subtraction process clearly:
- Start with the number 180.
- Subtract the given angle measure, in this case, 127.
- Perform the subtraction step-by-step: \[ 180 - 127 = 53 \]

This final number, 53, is the measure of the supplementary angle. Strengthening basic arithmetic skills is crucial for solving geometric problems effortlessly.

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