/*! 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 52 Can two complementary angles bot... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 52

Can two complementary angles both be obtuse? Why or why not?

Short Answer

Expert verified
No, two complementary angles cannot both be obtuse because their measures would exceed 90 degrees.

Step by step solution

01

- Understand Complementary Angles

Complementary angles are two angles whose measures add up to 90 degrees. Mathematically, if two angles \(a\) and \(b\) are complementary, then \(a + b = 90^\text{掳}\).
02

- Define Obtuse Angles

An obtuse angle is an angle that measures greater than 90 degrees but less than 180 degrees.
03

- Analyze the Possibility

Considering that a complementary angle must add up to 90 degrees, check if an obtuse angle can be part of this combination. Since an obtuse angle is greater than 90 degrees by definition, it's impossible for their sum to be 90 degrees. Therefore, two obtuse angles cannot add up to be complementary.

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.

Obtuse Angles
An obtuse angle is one that measures between 90 and 180 degrees. This means it is larger than a right angle (90 degrees) but smaller than a straight angle (180 degrees). Because of this property, an obtuse angle appears more 'open' or 'spread out' compared to a right angle or acute angle (which is less than 90 degrees).
To visualize an obtuse angle, think of the hands of a clock at 10:10. The angle between the hour and minute hands is obtuse.
Understanding this is crucial as it directly relates to why two obtuse angles can't be complementary. Since an obtuse angle is always larger than 90 degrees, adding another angle to it will always result in a sum greater than 90 degrees.
Angle Measurements
Angles are measured in degrees, a unit that ranges from 0 to 360. Here are some important types of angles commonly encountered:
  • Acute Angles: measure less than 90 degrees.
  • Right Angles: exactly 90 degrees.
  • Obtuse Angles: greater than 90 degrees but less than 180 degrees.
  • Straight Angles: exactly 180 degrees.
  • Reflex Angles: greater than 180 degrees.
Knowing the measurements allows us to categorize angles and understand how they interact. For instance, complementary angles always sum to 90 degrees, so they must each be less than or equal to 90 degrees.
Sum of Angles
When discussing angle sums, it's essential to understand that the combination of certain types of angles leads to specific total measurements. With complementary angles, their sum is always 90 degrees. This is a fixed rule.
When two angles are complementary, their measurements add up to form a right angle. If one angle is known, you can always find the other by subtracting the known angle from 90 degrees.
This property makes it clear why two obtuse angles can never be complementary. Each obtuse angle is already more than 90 degrees, and their sum will always exceed 180 degrees, making it impossible for any two obtuse angles to sum to 90 degrees.

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

Define the key terms. a. Rectangular solid b. Cube c. Right circular cylinder d. Right circular cone e. Sphere

Cliff drives his children to their sports activities outside of school. When he drives his son to baseball practice, it is a \(6-\mathrm{km}\) round trip. When he drives his daughter to basketball practice, it is a \(1800-\mathrm{m}\) round trip. If basketball practice is 3 times a week and baseball practice is twice a week, how many kilometers does Cliff drive?

Perform the conversions. $$50 \mathrm{mcg}=\mathrm{mg}$$

Simplify the squares and square roots. $$\sqrt{64}$$

A 26 -ft-long wire is to be tied from a stake in the ground to the top of a 24 -ft pole. How far from the bottom of the pole should the stake be placed?
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

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.