/*! 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 8 If \(\angle \mathrm{X}<\angle... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 15: Problem 8

If \(\angle \mathrm{X}<\angle \mathrm{Y},\) what is the relation between their complements?

Short Answer

Expert verified
The complement of \(\angle X\) is greater than the complement of \(\angle Y\).

Step by step solution

01

Understanding Complementary Angles

Complementary angles are two angles that add up to \(90^{o}\). If we consider one angle as A, its complement will be \(90^{o}\) - A. Therefore, if we have two angles, X and Y, their complements can be defined as \(90^{o}\) - X and \(90^{o}\) - Y
02

Comparing Angle X and Y

The problem states that \(\angle X<\angle Y\), or in other words, Angle X is smaller than Angle Y.
03

Finding Relation Between Complements of X and Y

If angle X is smaller than angle Y, it follows that its complement is greater than the complement of angle Y. This is because as the value of angle increases, the value of its complement decreases, since they add to 90. So, if \( \angle X<\angle Y \), then \( 90^{o}\) - X > \( 90^{o} \) - Y, or in other words, the complement of X is greater than the complement of Y.

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.

Angle Comparison
Comparing angles is a fundamental part of geometry. When we say one angle is smaller than another, we directly compare their degree measures. For example, in our exercise, we have
  • \( \angle X < \angle Y \)
This means that the measure (in degrees) of angle \(X\) is less than that of angle \(Y\). Generally, angles can be compared in the same unit (like degrees or radians) and a simple inequality can tell us their relationship.
Comparing angles helps us analyze geometric figures and solve complex problems, as it provides a clear picture of how angles balance each other out in a given shape.
Geometry Problem Solving
Solving geometry problems often involves understanding various relationships between angles and shapes. In our example, knowing the definition of complementary angles aids in problem-solving. Complementary angles sum up to
  • \(90^\circ \)
which means they can form a right angle together. In geometry, problem-solving might involve breaking down the problem into smaller parts, like understanding how the complements are calculated:
  • If \(\angle A\) is given, then its complement is \(90^\circ - \angle A\).
This approach, step by step, will help you determine relationships effectively and come to the correct conclusion. Always ensure to follow each step logically and verify your conclusions.
Angle Relationships
The relationship between angles goes beyond simple comparisons. Understanding complementary angles extends into many other components of geometry. For instance:
  • If \(\angle X < \angle Y\), then \(90^\circ - \angle X > 90^\circ - \angle Y\).
This is because as one angle increases, its complement decreases accordingly. Relationships like these are crucial as they are used in various geometric proofs and constructions. Think of it like a see-saw; when one side goes up, the other must go down. This lets us understand and solve problems involving angles in a straightforward manner, paving the way for deeper insights into the properties of geometric figures.

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

Solve \(x^{2}+x<6\)

If \(x<3\) and \(x \neq 3,\) what can be concluded about \(x ?\)

Solve \(18-3 x>3\) over the positive even integers.

Given: \(\overline{\mathrm{AB}} \| \overline{\mathrm{CD}}, \overline{\mathrm{AB}} \cong \overline{\mathrm{AD}}\) $$ \angle \mathrm{DAC}=75^{\circ}, \angle \mathrm{DCA}=45^{\circ} $$ Which is longer, \(\overline{\mathrm{BC}}\) or \(\overline{\mathrm{DC}} ?\) (IMAGE CAN'T COPY)

If \(x\) exceeds \(y\) by 5 and \(y\) exceeds \(z\) by \(3,\) how is \(x\) related to \(z ?\)
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

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.