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Chapter 8: Problem 44

The measure of an angle is given. Find the measure of the supplement. $$124^{\circ}$$

Short Answer

Expert verified
56掳

Step by step solution

01

- Define Supplementary Angles

Supplementary angles are two angles whose measures add up to 180 degrees. Therefore, if one angle is given, the supplementary angle can be found by subtracting the given angle from 180 degrees.
02

- Subtract the Given Angle from 180 degrees

To find the measure of the supplement of the given angle 124 degrees, subtract 124 degrees from 180 degrees:\[ 180^{\bullet} - 124^{\bullet} \]
03

- Perform the Subtraction

Perform the arithmetic to find the measure of the supplement:\[ 180^{\bullet} - 124^{\bullet} = 56^{\bullet} \]

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Key Concepts

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

Angle Measurement
Understanding angle measurements is fundamental in geometry. An angle is formed where two lines meet at a common point called the vertex. The measurement of an angle is typically given in degrees, symbolized by the degree sign 掳. There are different types of angles based on their measurements:
  • Acute angles: less than 90掳
  • Right angles: exactly 90掳
  • Obtuse angles: between 90掳 and 180掳
  • Straight angles: exactly 180掳
For this exercise, we are focusing on supplementary angles, meaning two angles that add up to 180掳. It's essential to first grasp how angles are measured and classified to solve problems involving these.
Subtraction
In the context of geometry, subtraction helps us find unknown angle measurements. For example, to find the supplementary angle of a given angle, you subtract the given angle from 180掳. This is straightforward arithmetic:
  • Write down the total sum of the angles, which is 180掳 for supplementary angles.
  • Subtract the given angle from this sum.
  • The result is the measure of the supplement.
In our exercise, we were given a 124掳 angle. The calculation performed was: \ \[ 180^\bullet - 124^\bullet \ \] This simple subtraction tells us that the supplementary angle is 56掳.
Degrees
Degrees are the units used to measure angles. The full range of possible degree measurements goes from 0掳 to 360掳. Common points to remember about degrees include:
  • 0掳 represents a completely closed angle.
  • 90掳 is a right angle, forming an L shape.
  • 180掳 is a straight line, making it the baseline for determining supplementary angles.
  • 360掳 completes a full circle.
In practical terms, degrees are very intuitive to visualize, making them ideal for learning and applying geometric principles. Knowing that 180掳 represents a straight angle is crucial when working with supplementary angles, as this forms the basis for performing the subtraction needed to find the unknown angle measurement.

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