/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 34 Find (if possible) the complemen... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 34

Find (if possible) the complement and the supplement of each angle. (a) \(130^{\circ}\) (b) \(170^{\circ}\)

Short Answer

Expert verified
The complements of the angles \(130^{\circ}\) and \(170^{\circ}\) do not exist as they would result in negative angles which aren't possible in this context. The supplements of the angles \(130^{\circ}\) and \(170^{\circ}\) are \(50^{\circ}\) and \(10^{\circ}\), respectively.

Step by step solution

01

Find the Complement for the given angle (if possible)

The complement of an angle \(A\) (in degrees) is given by the formula \(90^{\circ} - A\). Applying this formula to the angle of \(130^{\circ}\) leads to a negative result (-40), which means that \(130^{\circ}\) does not have a complement. Similarly, calculating the complement of \(170^{\circ}\) also leads to a negative result (\(-80^{\circ}\)), indicating that \(170^{\circ}\) also has no complement.
02

Find the Supplement for the given angle

The supplement of an angle \(A\) (in degrees) is given by the formula \(180^{\circ} - A\). Using this formula, the supplement of \(130^{\circ}\) is \(50^{\circ}\), and the supplement of \(170^{\circ}\) is \(10^{\circ}\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Complementary Angles
In geometry, complementary angles are two angles whose measures add up to exactly 90 degrees. Imagine turning a corner that's a perfect square; the angle you turn is 90 degrees, which is the hallmark of complementary angles. When you know one angle and need to find its complement, simply subtract the angle's measurement from 90 degrees.

However, an important detail to remember is that an individual angle larger than 90 degrees cannot have a complement. This is because subtracting any positive angle from 90 degrees would not leave enough degrees to form another angle. Therefore, the complements are always two angles that both are less than 90 degrees each.
Supplementary Angles
Moving on from corners to straight lines, we encounter the concept of supplementary angles. These are pairs of angles that together form a straight line, totaling 180 degrees. Like with complementary angles, if you know one angle and want to find its supplement, you subtract the angle鈥檚 measure from 180 degrees.

Unlike complements, even angles greater than 90 degrees have supplements because the sum of the angles is larger. In the exercise, we see that angles of 130 and 170 degrees both have supplements because there is room to add another angle to reach the 180-degree mark. This flexibility in angle size explains why any angle has a supplementary angle.
Angle Measurements
Understanding angle measurements is foundational in geometry. Angles are measured in degrees, and there are a few key benchmarks to remember. A right angle is 90 degrees, a straight angle is 180 degrees, and a full rotation forms a 360-degree angle, also known as a circle. Measuring angles allows us to describe and calculate properties of shapes and figures, providing context for concepts like complementary and supplementary angles.

When measuring angles, remember that negative measurements don't apply. That's why when we search for complements and supplements, we dismiss the negative results, as seen in the exercise with angles over 90 degrees attempting to find a complement.
Precalculus
In the broader realm of mathematics, Precalculus serves as a bridge between algebra and calculus. While Precalculus itself doesn't generally focus on angles, the understanding of these measures is crucial when climbing the mathematical ladder. Concepts like complementary and supplementary angles lay the groundwork for more advanced topics in trigonometry, which is often a significant component of a Precalculus course. Trigonometric functions such as sine, cosine, and tangent are based on angle measurements, making the exercise of finding supplementary and complementary angles relevant for students progressing through Precalculus.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

When tuning a piano, a technician strikes a tuning fork for the A above middle \(\mathrm{C}\) and sets up a wave motion that can be approximated by \(y=0.001 \sin 880 \pi t,\) where \(t\) is the time (in seconds). (a) What is the period of the function? (b) The frequency \(f\) is given by \(f=1 / p .\) What is the frequency of the note?

After exercising for a few minutes, a person has a respiratory cycle for which the velocity of airflow is approximated by $$v=1.75 \sin \frac{\pi t}{2}$$ where \(t\) is the time (in seconds). (Inhalation occurs when \(v > 0,\) and exhalation occurs when \(v < 0 .\) ) (a) Find the time for one full respiratory cycle. (b) Find the number of cycles per minute. (c) Sketch the graph of the velocity function.

Fill in the blank. If not possible, state the reason. As \(x \rightarrow-1^{+},\) the value of arccos \(x \rightarrow\) \(\square\).

Find a model for simple harmonic motion satisfying the specified conditions. $$\begin{array}{cc}\text{Displacement \((t=0)\)} & \text{Amplitude} & \text{Period} \\ 2 \mathrm{feet} & 2 \mathrm{feet}& 10 \mathrm{seconds}\end{array}$$

A Ferris wheel is built such that the height \(h\) (in feet) above ground of a seat on the wheel at time \(t\) (in seconds) can be modeled by $$h(t)=53+50 \sin \left(\frac{\pi}{10} t-\frac{\pi}{2}\right)$$ (a) Find the period of the model. What does the period tell you about the ride? (b) Find the amplitude of the model. What does the amplitude tell you about the ride? (c) Use a graphing utility to graph one cycle of the model.
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation

Logic and Functions

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.