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Chapter 3: Problem 6

Determine the measures of the complement and supplement of each angle. 79

Short Answer

Expert verified
The complement is 11 degrees and the supplement is 101 degrees.

Step by step solution

01

Define Complementary and Supplementary Angles

Complementary angles are two angles whose measures add up to 90 degrees. Supplementary angles are two angles whose measures add up to 180 degrees. To solve this exercise, we need to find the angles that sum with the given angle to get 90 degrees and 180 degrees, respectively.
02

Calculate the Complement of a 79-degree Angle

To find the complement of a 79-degree angle, subtract 79 from 90. This is expressed as: \[ 90 - 79 = 11 \] So, the measure of the complementary angle is 11 degrees.
03

Calculate the Supplement of a 79-degree Angle

To find the supplement of a 79-degree angle, subtract 79 from 180. This is shown as: \[ 180 - 79 = 101 \] Thus, the measure of the supplementary angle is 101 degrees.

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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 special because they always add up to 90 degrees. This means when you have two angles, and their sum is 90 degrees, they are considered complementary. These angles help us understand right angles better because a right angle is exactly 90 degrees.

Key facts about complementary angles:
  • Two angles are complementary if their measures add up to 90 degrees.
  • You can find one complementary angle if you know the other by subtracting the known angle from 90.
  • If one angle measures 79 degrees, to find its complement, simply calculate: \(90 - 79 = 11\). Therefore, the complement is 11 degrees.
Remembering these basics can help when solving geometry problems involving right-angled triangles or adjacent angles that add up to 90 degrees.
Supplementary Angles
In contrast to complementary angles, supplementary angles have a total measure of 180 degrees. These angles are significant because they form a straight line when placed next to each other.

Here鈥檚 what you need to know about supplementary angles:
  • Two angles are supplementary if their measures sum up to 180 degrees.
  • If you need to determine one angle that is supplementary to another, subtract the known angle's measure from 180.
  • For an angle measuring 79 degrees, its supplementary angle is calculated as: \(180 - 79 = 101\). Thus, 101 degrees is the supplement of 79 degrees.
The concept of supplementary angles is frequently used in analyzing polygons, particularly when discussing angles around a point or on a line.
Angle Measurements
Angle measurements are fundamental in geometry and help us understand the size of an angle. Angles are measured in degrees, and there are different types based on their measurements.

Here are the essentials of angle measurements:
  • An angle less than 90 degrees is called an acute angle.
  • An angle exactly 90 degrees is a right angle, often seen in squares and rectangles.
  • Angles greater than 90 degrees but less than 180 degrees are obtuse angles.
  • A 180-degree angle forms a straight line, known as a straight angle.
  • Being able to measure and identify these angles aids in understanding the relationships between angles, like complementary and supplementary angles.
Learning to measure angles helps in solving various math problems and is a skill used in many real-life applications, like construction and design.

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Most popular questions from this chapter

Use a protractor to draw an angle having each measurement. Then classify each angle as acute, obtuse, or right. \(26^{\circ}\)

Use a protractor to draw an angle having each measurement. Then classify each angle as acute, obtuse, or right. \(115^{\circ}\)

Find the measure of an angle that is complementary to \(\angle B\) if \(\angle B \cong \angle E\) and \(m \angle E=43\).

Draw and label a coordinate plane. Then graph and label point \(C\) at \((-5,3)\). (Lesson 2-4)

\(\overleftrightarrow{B N} \perp \overleftrightarrow{R T}, \overleftrightarrow{M N} \perp \overleftrightarrow{A B}\), and point \(T\) is the midpoint of \(\overline{N B}\). Determine whether each of the following is true or false. \(\overline{N T} \cong \overline{B T}\)
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