/*! 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 33 MODELING WITH MATHEMATIG脽 base ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 33

MODELING WITH MATHEMATIG脽 base of a jewelry box is shaped like a regular hexagon. What is the measure of each interior angle of the jewelry box base?

Short Answer

Expert verified
The measure of each interior angle of the jewelry box base, a regular hexagon, is \(120\) degrees.

Step by step solution

01

Identify the number of sides

Identify that a hexagon has 6 sides. Let's represent it as \(n\). So, \(n = 6\).
02

Use the formula to calculate the total interior angles

Use the formula \(180(n-2)\) to calculate the total interior angles of the hexagon. Substitute \(n = 6\) in the formula: \(180(6-2) = 720\)
03

Calculate the measure of each interior angle

Since it is a regular hexagon, all the interior angles are equal. So, to calculate the measure of each angle, divide the total by the number of angles (which is equal to the number of sides, 6 in this case). \(720/6 = 120\).

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.

Understanding Interior Angles
Interior angles are the angles found on the inside of a polygon and are formed by two adjacent sides. When dealing with interior angles, it's essential to know that the sum of these angles depends on the number of sides of the polygon. For any polygon, the formula to find the sum of its interior angles is \(180(n - 2)\), where \(n\) is the number of sides. This formula helps in understanding how each interior angle contributes to the overall shape of the polygon. In regular polygons, each interior angle has an equal measure, making calculations straightforward and more predictable. It's crucial to remember this distinction when working with different types of polygons as it will affect how you solve for unknown angles.
Exploring Regular Polygons
A regular polygon is a polygon with all sides and angles equal. These characteristics simplify many geometric calculations. For instance, in a regular polygon, once you know the sum of the interior angles, you can easily calculate the measure of each angle by dividing the total sum by the number of sides. Regular polygons are symmetric and are often used in design and modeling due to their balanced appearance.
  • The symmetry and consistency make regular polygons a popular choice in architectural and design projects.
  • The regularity allows for straightforward calculations and predictions in geometric and trigonometric problems.
  • Examples of regular polygons include equilateral triangles, squares, and regular pentagons.
Regular polygons like a hexagon are simple yet powerful shapes in geometry, enabling complex structures and models.
Hexagon's Unique Features
A hexagon is a polygon with six sides. Regular hexagons are widely used due to their unique property of tiling without gaps, which is evident in beehives and certain flooring patterns. In geometry, hexagons are valued for their ability to cover a plane efficiently. When it comes to the interior angles of a regular hexagon, each angle measures 120 degrees. This is because the total sum of all interior angles in a hexagon is 720 degrees, as derived from the formula \(180(n-2)\), where \(n\) is 6. By dividing 720 degrees by the 6 angles, you find that each interior angle equals 120 degrees.
  • Hexagons maximize space efficiently, fitting together perfectly without gaps.
  • They offer structural integrity, making them useful in both natural and man-made structures.
  • Regular hexagons combine complexity with elegance, offering diverse applications in math and science.
Understanding hexagons can enhance your grasp of geometry and its practical applications.

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

THOUGHT PROVOKING Create a regular hexagon using congruent parallelograms.

PROVING A THEOREM Use the plan for proof below to write a paragraph proof for one part of the Rhombus Diagonals Theorem (Theorem 7.11). Given ABCD is a parallelogram. \(\overline{\mathrm{AC}} \perp \overline{\mathrm{BD}}\) Prove ABCD is a rhombus. Plan for Proof Because ABCD is a parallelogram, its diagonals bisect each other at \(X\) Use \(\overline{A C} \perp \overline{~ B D}\) to show that \(\Delta \mathrm{BXC} \cong \triangle \mathrm{DXC}\) . Then show that \(\overline{\mathrm{BC}} \cong \overline{\mathrm{DC} .}\) Use the properties of a parallelogram to show that ABCD is a rhombus.

WRITING A FORMUL. AVrite a formula to nd the number of sides \(n\) in a regular polygon given that the measure of one exterior angle is \(x^{\circ}\) .

In Exercises \(55-60\) , decide whether \(JKLM\) is a rectangle, a rhombus, or a square. Give all names that apply. Explain your reasoning. $$ \mathrm{J}(-2,7), \mathrm{K}(7,2), \mathrm{L}(-2,-3), \mathrm{M}(-11,2) $$

In quadrilateral ABCD \(\mathrm{m} \angle \mathrm{B}=124^{\circ}, \mathrm{m} \angle \mathrm{A}=56^{\circ},\) and \(\mathrm{m} \angle \mathrm{C}=124^{\circ}\) Your friend claims quadrilateral ABCD could be a parallelogram. Is your friend correct? Explain your reasoning.
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

Read Explanation

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Calculus

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.