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Chapter 8: Problem 33

The measure of an angle is given. Find the measure of the complement. $$80^{\circ}$$

Short Answer

Expert verified
10 degrees

Step by step solution

01

- Understand Complementary Angles

Complementary angles are two angles whose measures add up to 90 degrees. Therefore, if you have the measure of one angle, you can find the measure of its complement by subtracting the given angle from 90 degrees.
02

- Apply the Formula

Given that the measure of one angle is 80 degrees, use the formula for complementary angles: \[ \text{Complement of an angle} = 90^{\text{掳}} - \text{Given angle} \]Substitute 80 degrees into the formula.
03

- Calculate the Complement

Perform the subtraction: \[ 90^{\text{掳}} - 80^{\text{掳}} = 10^{\text{掳}} \]

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Key Concepts

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

Angle Subtraction
Angle subtraction is a key concept for understanding complementary angles. To find the complement of an angle, you subtract the given angle from 90 degrees. For example, if you have an angle that measures 80 degrees,
you would use the formula for complementary angles: \ \text{Complement of an angle} = 90^{\text{掳}} - \text{Given angle}.
In this case, you would substitute 80 degrees into the formula:
\ \text{Complement of 80^{\text{掳}} = 90^{\text{掳}} - 80^{\text{掳}}}.
Performing the subtraction, you get the complement:
\[ 90^{\text{掳}} - 80^{\text{掳}} = 10^{\text{掳}} \]. Therefore, the complementary angle is 10 degrees.

Keep in mind:
  • The subtraction is always done from 90 degrees.

  • If the given angle is greater than 90 degrees, it cannot have a complement because complementary angles must always sum to exactly 90 degrees.
Geometry Basics
In geometry, understanding basic concepts like complementary angles is crucial. Complementary angles are a specific type of angle pair
that add up to form a right angle, which measures exactly 90 degrees. This is an essential concept in various geometric problems and constructions.

Some important points to remember:
  • A right angle is always 90 degrees.

  • Two angles are complementary if their sum is 90 degrees, regardless of the individual measures.

  • If you have one angle, you can always find the complementary angle by subtracting from 90 degrees (using angle subtraction).

These concepts are foundational and widely applicable in fields ranging from basic geometry to advanced trigonometry and even in certain aspects of physics.
Angle Measurement
Angle measurement is the process of determining the size of an angle in degrees. The degree is a unit of measurement for angles, where a full circle is 360 degrees.
A right angle, as mentioned before, is 90 degrees.

Here are some helpful points about angle measurement:
  • To find the measure of a complementary angle, you start with a right angle, which is 90 degrees, and subtract the measure of the given angle.

  • When using a protractor, align the baseline with one side of the angle and read the degree measure where the other side intersects the protractor.

  • Always double-check your measurements to ensure accuracy.

Accurate angle measurement is essential for solving geometric problems and ensuring the precision needed in fields like engineering, architecture, and various other scientific disciplines.

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