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Chapter 1: Problem 38

What is the supplement of the complement of an angle measuring \(50^{\circ} ?\)

Short Answer

Expert verified
140 degrees

Step by step solution

01

- Understand Complements

The complement of an angle is the amount you must add to it to get a total of 90 degrees. For an angle measuring \(50^{\circ}\), the complement is \(90^{\circ} - 50^{\circ}\).
02

- Calculate the Complement

Calculate the complement by performing the subtraction: \(90^{\circ} - 50^{\circ} = 40^{\circ}\). So the complement of a \(50^{\circ}\) angle is \(40^{\circ}\).
03

- Understand Supplements

The supplement of an angle is the amount you must add to it to get a total of 180 degrees. For an angle that measures \(40^{\circ}\), we need to find the supplement.
04

- Calculate the Supplement

Calculate the supplement by performing the subtraction: \(180^{\circ} - 40^{\circ}\). By calculating, we get \(180^{\circ} - 40^{\circ} = 140^{\circ}\).

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Key Concepts

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

Complementary Angles
Complementary angles are two angles that add up to 90 degrees.
Think of it as a pair of angles that complete each other to form a right angle.
For instance, if you have an angle measuring 50 degrees, its complement is found by calculating: \[90^\text{掳} - 50^\text{掳} = 40^\text{掳}\]
This means 50 degrees and 40 degrees together make a right angle.
Complementary angles are particularly useful in various geometry problems and they help understand angle relationships in shapes.
Supplementary Angles
Supplementary angles are two angles that add up to 180 degrees.
It's like two angles that together form a straight line.
When you have an angle like 40 degrees, the supplement can be found by calculating: \[180^\text{掳} - 40^\text{掳} = 140^\text{掳}\]
So, 40 degrees and 140 degrees create a straight line together.
Knowing about supplementary angles helps you solve many problems related to line segments and polygon properties.
Angle Measurement
Angle measurement is essential in geometry because it allows you to describe the size of an angle.
Angles are measured in degrees, where a full circle is 360 degrees.
Different types of angles include:
  • 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 complementary and supplementary angles, you need to measure the initial angle correctly.
This is why understanding angle measurement helps you accurately solve various geometric and real-life problems.

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