McDougal Littell Jurgensen Geometry: Student Edition Geometry

5th Edition

ISBN: 9780395977279

Author: Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

Publisher: Houghton Mifflin Company College Division

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Question

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

Chapter 3.6, Problem 30WE

(a)

To determine

To find: The sum of measure of the angles formed at the tips of five-pointed star.

(a)

Expert Solution

Answer to Problem 30WE

The sum of measures of the angles formed at the tips of five-pointed star is 180°.

Explanation of Solution

Given:

McDougal Littell Jurgensen Geometry: Student Edition Geometry, Chapter 3.6, Problem 30WE , additional homework tip 1

Consider a 5-point star as shown in the below figure:

McDougal Littell Jurgensen Geometry: Student Edition Geometry, Chapter 3.6, Problem 30WE , additional homework tip 2

The sum of the interior angles of a pentagon is always 540°.

The exterior point angle is always equal to the sum of adjacent interior angles - 180°.

The angles of the triangle are 180 - A, 180 - B, X. By definition of angles of a triangle, X is equal to

180∘−(180∘−A)−(180∘−B)=A+B−180∘ .

Each interior angle of the pentagon is used twice, and there are 5 points, so

(2×540)−(5×180)=180°

Therefore, the sum of measures of the angles formed at the tips of star is 180°.

(b)

To determine

To Find: The sum of measures of the angles formed at the tips of six-pointed star.

(b)

Expert Solution

Answer to Problem 30WE

The sum of measures of the angles formed at the tips of six-pointed star is 360° .

Explanation of Solution

Given:

McDougal Littell Jurgensen Geometry: Student Edition Geometry, Chapter 3.6, Problem 30WE , additional homework tip 3

Consider a six-pointed star as shown below.

McDougal Littell Jurgensen Geometry: Student Edition Geometry, Chapter 3.6, Problem 30WE , additional homework tip 4

The sum is equal to 360° as it is composed of 2 triangles.

Thus, 180+180=360.

Therefore, the sum of measures of the angles formed at the tips of star is 360°.

(c)

To determine

To find: The sum of the angles measures at the tips of an n-pointed star with the help of inductive reasoning.

(c)

Expert Solution

Answer to Problem 30WE

By inductive reasoning it is conclude that for n-pointed star, the sum of the angles formed at the tip of star is n·180°–720° for n > 4 .

Explanation of Solution

The sum of the angles formed at the tips of 5 pointed star is 180°, which can be written as

5·180°–720° =900°–720° =180°

The sum of the angles formed at the tips of 6 pointed star is 360°, which can be written as

6·180°–720° =1080°–720° =360°

(d)

To determine

To justify: The formula by using deductive reasoning.

(d)

Expert Solution

Explanation of Solution

A 6-point star is formed by 2 triangles, so the sum of the angles of two triangles is 360∘ .

It is given that the measurement of n vertex of the angle plus the sum of the all exterior angle equals to n⋅180∘ .

There are always 2 exterior angles for n-pointed star whose sum is 360∘ .

The sum of the angles formed at the tips of n point star is n⋅180∘−720∘ .

Chapter 3.6, Problem 29WE

Chapter 3.6, Problem 1ST2

Chapter 3 Solutions

McDougal Littell Jurgensen Geometry: Student Edition Geometry

Ch. 3.1 - Prob. 1CE Ch. 3.1 - Prob. 2CE Ch. 3.1 - Prob. 3CE Ch. 3.1 - Prob. 4CE Ch. 3.1 - Prob. 5CE Ch. 3.1 - Prob. 6CE Ch. 3.1 - Prob. 7CE Ch. 3.1 - Prob. 8CE Ch. 3.1 - Prob. 9CE Ch. 3.1 - Prob. 10CE

Ch. 3.1 - Prob. 11CE Ch. 3.1 - Prob. 12CE Ch. 3.1 - Prob. 13CE Ch. 3.1 - Prob. 14CE Ch. 3.1 - Prob. 15CE Ch. 3.1 - Prob. 16CE Ch. 3.1 - Prob. 17CE Ch. 3.1 - Prob. 18CE Ch. 3.1 - Prob. 19CE Ch. 3.1 - Prob. 1WE Ch. 3.1 - Prob. 2WE Ch. 3.1 - Prob. 3WE Ch. 3.1 - Prob. 4WE Ch. 3.1 - Prob. 5WE Ch. 3.1 - Prob. 6WE Ch. 3.1 - Prob. 7WE Ch. 3.1 - Prob. 8WE Ch. 3.1 - Prob. 9WE Ch. 3.1 - Prob. 10WE Ch. 3.1 - Prob. 11WE Ch. 3.1 - Prob. 12WE Ch. 3.1 - Prob. 13WE Ch. 3.1 - Prob. 14WE Ch. 3.1 - Prob. 15WE Ch. 3.1 - Prob. 16WE Ch. 3.1 - Prob. 17WE Ch. 3.1 - Prob. 18WE Ch. 3.1 - Prob. 19WE Ch. 3.1 - Prob. 20WE Ch. 3.1 - Prob. 21WE Ch. 3.1 - Prob. 22WE Ch. 3.1 - Prob. 23WE Ch. 3.1 - Prob. 24WE Ch. 3.1 - Prob. 25WE Ch. 3.1 - Prob. 26WE Ch. 3.1 - Prob. 27WE Ch. 3.1 - Prob. 28WE Ch. 3.1 - Prob. 29WE Ch. 3.1 - Prob. 30WE Ch. 3.1 - Prob. 31WE Ch. 3.1 - Prob. 32WE Ch. 3.1 - Prob. 33WE Ch. 3.1 - Prob. 34WE Ch. 3.1 - Prob. 35WE Ch. 3.1 - Prob. 36WE Ch. 3.1 - Prob. 37WE Ch. 3.1 - Prob. 38WE Ch. 3.1 - Prob. 39WE Ch. 3.1 - Prob. 40WE Ch. 3.1 - Prob. 41WE Ch. 3.1 - Prob. 42WE Ch. 3.2 - Prob. 1CE Ch. 3.2 - Prob. 2CE Ch. 3.2 - Prob. 3CE Ch. 3.2 - Prob. 4CE Ch. 3.2 - Prob. 5CE Ch. 3.2 - Prob. 6CE Ch. 3.2 - Prob. 7CE Ch. 3.2 - Prob. 8CE Ch. 3.2 - Prob. 9CE Ch. 3.2 - Prob. 10CE Ch. 3.2 - Prob. 11CE Ch. 3.2 - Prob. 12CE Ch. 3.2 - Prob. 13CE Ch. 3.2 - Prob. 14CE Ch. 3.2 - Prob. 1WE Ch. 3.2 - Prob. 2WE Ch. 3.2 - Prob. 3WE Ch. 3.2 - Prob. 4WE Ch. 3.2 - Prob. 5WE Ch. 3.2 - Prob. 6WE Ch. 3.2 - Prob. 7WE Ch. 3.2 - Prob. 8WE Ch. 3.2 - Prob. 9WE Ch. 3.2 - Prob. 10WE Ch. 3.2 - Prob. 11WE Ch. 3.2 - Prob. 12WE Ch. 3.2 - Prob. 13WE Ch. 3.2 - Prob. 14WE Ch. 3.2 - Prob. 15WE Ch. 3.2 - Prob. 16WE Ch. 3.2 - Prob. 17WE Ch. 3.2 - Prob. 18WE Ch. 3.2 - Prob. 19WE Ch. 3.2 - Prob. 20WE Ch. 3.2 - Prob. 21WE Ch. 3.2 - Prob. 22WE Ch. 3.2 - Prob. 23WE Ch. 3.2 - Prob. 24WE Ch. 3.2 - Prob. 25WE Ch. 3.2 - Prob. 1MRE Ch. 3.2 - Prob. 2MRE Ch. 3.2 - Prob. 3MRE Ch. 3.2 - Prob. 4MRE Ch. 3.3 - Prob. 1CE Ch. 3.3 - Prob. 2CE Ch. 3.3 - Prob. 3CE Ch. 3.3 - Prob. 4CE Ch. 3.3 - Prob. 5CE Ch. 3.3 - Prob. 6CE Ch. 3.3 - Prob. 7CE Ch. 3.3 - Prob. 8CE Ch. 3.3 - Prob. 9CE Ch. 3.3 - Prob. 10CE Ch. 3.3 - Prob. 11CE Ch. 3.3 - Prob. 12CE Ch. 3.3 - Prob. 13CE Ch. 3.3 - Prob. 14CE Ch. 3.3 - Prob. 15CE Ch. 3.3 - Prob. 16CE Ch. 3.3 - Prob. 17CE Ch. 3.3 - Prob. 18CE Ch. 3.3 - Prob. 19CE Ch. 3.3 - Prob. 20CE Ch. 3.3 - Prob. 1WE Ch. 3.3 - Prob. 2WE Ch. 3.3 - Prob. 3WE Ch. 3.3 - Prob. 4WE Ch. 3.3 - Prob. 5WE Ch. 3.3 - Prob. 6WE Ch. 3.3 - Prob. 7WE Ch. 3.3 - Prob. 8WE Ch. 3.3 - Prob. 9WE Ch. 3.3 - Prob. 10WE Ch. 3.3 - Prob. 11WE Ch. 3.3 - Prob. 12WE Ch. 3.3 - Prob. 13WE Ch. 3.3 - Prob. 14WE Ch. 3.3 - Prob. 15WE Ch. 3.3 - Prob. 16WE Ch. 3.3 - Prob. 17WE Ch. 3.3 - Prob. 18WE Ch. 3.3 - Prob. 19WE Ch. 3.3 - Prob. 20WE Ch. 3.3 - Prob. 21WE Ch. 3.3 - Prob. 22WE Ch. 3.3 - Prob. 23WE Ch. 3.3 - Prob. 24WE Ch. 3.3 - Prob. 25WE Ch. 3.3 - Prob. 26WE Ch. 3.3 - Prob. 27WE Ch. 3.3 - Prob. 28WE Ch. 3.3 - Prob. 29WE Ch. 3.3 - Prob. 30WE Ch. 3.3 - Prob. 31WE Ch. 3.3 - Prob. 1ST1 Ch. 3.3 - Prob. 2ST1 Ch. 3.3 - Prob. 3ST1 Ch. 3.3 - Prob. 4ST1 Ch. 3.3 - Prob. 5ST1 Ch. 3.3 - Prob. 6ST1 Ch. 3.3 - Prob. 7ST1 Ch. 3.3 - Prob. 8ST1 Ch. 3.3 - Prob. 9ST1 Ch. 3.3 - Prob. 10ST1 Ch. 3.3 - Prob. 11ST1 Ch. 3.3 - Prob. 12ST1 Ch. 3.3 - Prob. 13ST1 Ch. 3.3 - Prob. 14ST1 Ch. 3.3 - Prob. 15ST1 Ch. 3.3 - Prob. 16ST1 Ch. 3.3 - Prob. 1E Ch. 3.3 - Prob. 2E Ch. 3.3 - Prob. 3E Ch. 3.3 - Prob. 4E Ch. 3.3 - Prob. 5E Ch. 3.3 - Prob. 6E Ch. 3.3 - Prob. 7E Ch. 3.3 - Prob. 8E Ch. 3.4 - Prob. 1CE Ch. 3.4 - Prob. 2CE Ch. 3.4 - Prob. 3CE Ch. 3.4 - Prob. 4CE Ch. 3.4 - Prob. 5CE Ch. 3.4 - Prob. 6CE Ch. 3.4 - Prob. 7CE Ch. 3.4 - Prob. 8CE Ch. 3.4 - Prob. 9CE Ch. 3.4 - Prob. 10CE Ch. 3.4 - Prob. 11CE Ch. 3.4 - Prob. 12CE Ch. 3.4 - Prob. 13CE Ch. 3.4 - Prob. 14CE Ch. 3.4 - Prob. 15CE Ch. 3.4 - Prob. 16CE Ch. 3.4 - Prob. 17CE Ch. 3.4 - Prob. 1WE Ch. 3.4 - Prob. 2WE Ch. 3.4 - Prob. 3WE Ch. 3.4 - Prob. 4WE Ch. 3.4 - Prob. 5WE Ch. 3.4 - Prob. 6WE Ch. 3.4 - Prob. 7WE Ch. 3.4 - Prob. 8WE Ch. 3.4 - Prob. 9WE Ch. 3.4 - Prob. 10WE Ch. 3.4 - Prob. 11WE Ch. 3.4 - Prob. 12WE Ch. 3.4 - Prob. 13WE Ch. 3.4 - Prob. 14WE Ch. 3.4 - Prob. 15WE Ch. 3.4 - Prob. 16WE Ch. 3.4 - Prob. 17WE Ch. 3.4 - Prob. 18WE Ch. 3.4 - Prob. 19WE Ch. 3.4 - Prob. 20WE Ch. 3.4 - Prob. 21WE Ch. 3.4 - Prob. 22WE Ch. 3.4 - Prob. 23WE Ch. 3.4 - Prob. 24WE Ch. 3.4 - Prob. 25WE Ch. 3.4 - Prob. 26WE Ch. 3.4 - Prob. 27WE Ch. 3.4 - Prob. 28WE Ch. 3.4 - Prob. 29WE Ch. 3.4 - Prob. 30WE Ch. 3.4 - Prob. 31WE Ch. 3.4 - Prob. 32WE Ch. 3.4 - Prob. 33WE Ch. 3.4 - Prob. 34WE Ch. 3.5 - Prob. 1CE Ch. 3.5 - Prob. 2CE Ch. 3.5 - Prob. 3CE Ch. 3.5 - Prob. 4CE Ch. 3.5 - Prob. 5CE Ch. 3.5 - Prob. 6CE Ch. 3.5 - Prob. 7CE Ch. 3.5 - Prob. 8CE Ch. 3.5 - Prob. 9CE Ch. 3.5 - Prob. 1WE Ch. 3.5 - Prob. 2WE Ch. 3.5 - Prob. 3WE Ch. 3.5 - Prob. 4WE Ch. 3.5 - Prob. 5WE Ch. 3.5 - Prob. 6WE Ch. 3.5 - Prob. 7WE Ch. 3.5 - Prob. 8WE Ch. 3.5 - Prob. 9WE Ch. 3.5 - Prob. 10WE Ch. 3.5 - Prob. 11WE Ch. 3.5 - Prob. 12WE Ch. 3.5 - Prob. 13WE Ch. 3.5 - Prob. 14WE Ch. 3.5 - Prob. 15WE Ch. 3.5 - Prob. 16WE Ch. 3.5 - Prob. 17WE Ch. 3.5 - Prob. 18WE Ch. 3.5 - Prob. 19WE Ch. 3.5 - Prob. 20WE Ch. 3.5 - Prob. 21WE Ch. 3.5 - Prob. 22WE Ch. 3.5 - Prob. 23WE Ch. 3.5 - Prob. 24WE Ch. 3.5 - Prob. 25WE Ch. 3.5 - Prob. 26WE Ch. 3.5 - Prob. 27WE Ch. 3.5 - Prob. 28WE Ch. 3.6 - Prob. 1CE Ch. 3.6 - Prob. 2CE Ch. 3.6 - Prob. 3CE Ch. 3.6 - Prob. 4CE Ch. 3.6 - Prob. 5CE Ch. 3.6 - Prob. 6CE Ch. 3.6 - Prob. 1WE Ch. 3.6 - Prob. 2WE Ch. 3.6 - Prob. 3WE Ch. 3.6 - Prob. 4WE Ch. 3.6 - Prob. 5WE Ch. 3.6 - Prob. 6WE Ch. 3.6 - Prob. 7WE Ch. 3.6 - Prob. 8WE Ch. 3.6 - Prob. 9WE Ch. 3.6 - Prob. 10WE Ch. 3.6 - Prob. 11WE Ch. 3.6 - Prob. 12WE Ch. 3.6 - Prob. 13WE Ch. 3.6 - Prob. 14WE Ch. 3.6 - Prob. 15WE Ch. 3.6 - Prob. 16WE Ch. 3.6 - Prob. 17WE Ch. 3.6 - Prob. 18WE Ch. 3.6 - Prob. 19WE Ch. 3.6 - Prob. 20WE Ch. 3.6 - Prob. 21WE Ch. 3.6 - Prob. 22WE Ch. 3.6 - Prob. 23WE Ch. 3.6 - Prob. 24WE Ch. 3.6 - Prob. 25WE Ch. 3.6 - Prob. 26WE Ch. 3.6 - Prob. 27WE Ch. 3.6 - Prob. 28WE Ch. 3.6 - Prob. 29WE Ch. 3.6 - Prob. 30WE Ch. 3.6 - Prob. 1ST2 Ch. 3.6 - Prob. 2ST2 Ch. 3.6 - Prob. 3ST2 Ch. 3.6 - Prob. 4ST2 Ch. 3.6 - Prob. 5ST2 Ch. 3.6 - Prob. 6ST2 Ch. 3.6 - Prob. 7ST2 Ch. 3.6 - Prob. 8ST2 Ch. 3.6 - Prob. 9ST2 Ch. 3.6 - Prob. 10ST2 Ch. 3.6 - Prob. 11ST2 Ch. 3.6 - Prob. 12ST2 Ch. 3.6 - Prob. 13ST2 Ch. 3.6 - Prob. 14ST2 Ch. 3.6 - Prob. 15ST2 Ch. 3 - Prob. 1CR Ch. 3 - Prob. 2CR Ch. 3 - Prob. 3CR Ch. 3 - Prob. 4CR Ch. 3 - Prob. 5CR Ch. 3 - Prob. 6CR Ch. 3 - Prob. 7CR Ch. 3 - Prob. 8CR Ch. 3 - Prob. 9CR Ch. 3 - Prob. 10CR Ch. 3 - Prob. 11CR Ch. 3 - Prob. 12CR Ch. 3 - Prob. 13CR Ch. 3 - Prob. 14CR Ch. 3 - Prob. 15CR Ch. 3 - Prob. 16CR Ch. 3 - Prob. 17CR Ch. 3 - Prob. 18CR Ch. 3 - Prob. 19CR Ch. 3 - Prob. 20CR Ch. 3 - Prob. 21CR Ch. 3 - Prob. 1CT Ch. 3 - Prob. 2CT Ch. 3 - Prob. 3CT Ch. 3 - Prob. 4CT Ch. 3 - Prob. 5CT Ch. 3 - Prob. 6CT Ch. 3 - Prob. 7CT Ch. 3 - Prob. 8CT Ch. 3 - Prob. 9CT Ch. 3 - Prob. 10CT Ch. 3 - Prob. 11CT Ch. 3 - Prob. 12CT Ch. 3 - Prob. 13CT Ch. 3 - Prob. 14CT Ch. 3 - Prob. 1AR Ch. 3 - Prob. 2AR Ch. 3 - 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