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Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584

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Chapter
Section
BuyFindarrow_forward

Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584
Chapter 7.2, Problem 43ES
Textbook Problem
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Given that m a = 95 ° and m b = 70 ° , find the measures of angles x and y.

Chapter 7.2, Problem 43ES, Given that ma=95 and mb=70, find the measures of angles x and y.

To determine

To find the measures of angles x and y.

Explanation of Solution

Given information:

Given, ma=95° and mb=70°.

  

Calculation:

From the given figure, it is evident that the angles mb and my are vertical angles

So, my=mb

Plugging the value mb=70° in the above equation,

  my=70°

Let the other interior angles in the triangle be ma' and mx' as shown in the figure above.

From the figure, ma' and ma form the supplementary angles

So, ma+ma'=180°

  ma+ma'ma=180°ma

  ma'=180°ma

Plugging the value ma=95° in the above equation, we get,

  ma'=180°95°

  ma'=85°

Sum of all the angles in the triangle is 180°.

So, ma'+mx'+mb=180°

Plugging the value ma'=85° and mb=70° in the above equation

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Chapter 7 Solutions

Mathematical Excursions (MindTap Course List)
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Ch. 7.1 - Convert between the two measurements. 712 lb = ozCh. 7.1 - Convert between the two measurements. 45 ton = lbCh. 7.1 - Convert between the two measurements. 212 c = fl...Ch. 7.1 - Convert between the two measurements. 10 qt = galCh. 7.1 - Convert between the two measurements. 7 gal = ptCh. 7.1 - Convert between the two measurements. 112 qt = cCh. 7.1 - Convert between the two measurements. 62 cm = mmCh. 7.1 - Convert between the two measurements. 6804 m = kmCh. 7.1 - Convert between the two measurements. 3.21 m = cmCh. 7.1 - Convert between the two measurements. 260 cm = mCh. 7.1 - Convert between the two measurements. 7421 g = kgCh. 7.1 - Convert between the two measurements. 43 mg = gCh. 7.1 - Convert between the two measurements. 0.45 g = dgCh. 7.1 - Convert between the two measurements. 0.0456 g =...Ch. 7.1 - Convert between the two measurements. 7.5 ml = LCh. 7.1 - Convert between the two measurements. 0.037 L = mlCh. 7.1 - Convert between the two measurements. 0.435 L =...Ch. 7.1 - Convert between the two measurements. 897 L =...Ch. 7.1 - Solve. 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For...Ch. 7.6 - Convert radian measure to degree measure. For...Ch. 7.6 - Convert radian measure to degree measure. For...Ch. 7.7 - Place two points A and B on a paper cup so that A...Ch. 7.7 - The only geodesics of a sphere are great circles....Ch. 7.7 - Write a sentence that explains how you know that...Ch. 7.7 - Excursion Exercises 4 to 6 require a world globe...Ch. 7.7 - Excursion Exercises 4 to 6 require a world globe...Ch. 7.7 - Excursion Exercises 4 to 6 require a world globe...Ch. 7.7 - The yellow surface at the left above is called a...Ch. 7.7 - State the parallel postulate for each of the...Ch. 7.7 - Name the mathematician who is called the...Ch. 7.7 - Name the mathematician who was the first to...Ch. 7.7 - What is the maximum number of right angles a...Ch. 7.7 - What name did Lobachevsky give to the geometry...Ch. 7.7 - Explain why great circles in Riemannian geometry...Ch. 7.7 - What is a geodesic?Ch. 7.7 - In which geometry can two distinct lines be...Ch. 7.7 - What model was used in this text to illustrate...Ch. 7.7 - In which geometry do all perpendiculars to a given...Ch. 7.7 - Find the exact area of a spherical triangle with...Ch. 7.7 - Find the area of a spherical triangle with three...Ch. 7.7 - City Geometry Find the Euclidean distance between...Ch. 7.7 - City Geometry Find the Euclidean distance between...Ch. 7.7 - City Geometry Find the Euclidean distance between...Ch. 7.7 - City Geometry Find the Euclidean distance between...Ch. 7.7 - City Geometry Find the Euclidean distance between...Ch. 7.7 - City Geometry Find the Euclidean distance between...Ch. 7.7 - City Geometry Find the Euclidean distance between...Ch. 7.7 - City Geometry Find the Euclidean distance between...Ch. 7.7 - A Distance Conversion Formula The following...Ch. 7.7 - A Distance Conversion Formula The following...Ch. 7.7 - A Distance Conversion Formula The following...Ch. 7.7 - A Distance Conversion Formula The following...Ch. 7.7 - A Distance Conversion Formula The following...Ch. 7.7 - A Distance Conversion Formula The following...Ch. 7.7 - Explain why there is no formula that can be used...Ch. 7.7 - a. If dE(P,Q)=dE(R,S), must dC(P,Q)=dC(R,S)?...Ch. 7.7 - Plot the points in the city circle with center...Ch. 7.7 - Plot the points in the city circle with center...Ch. 7.7 - Plot the points in the city circle with center (0,...Ch. 7.7 - Plot the points in the city circle with center (0,...Ch. 7.7 - How many points are on the city circle with center...Ch. 7.7 - Which of the following city circles has the most...Ch. 7.7 - Apartment Hunting in a City Use the following...Ch. 7.7 - Apartment Hunting in a City Use the following...Ch. 7.7 - A Finite Geometry Consider a finite geometry with...Ch. 7.7 - A Finite Geometry Consider a finite geometry with...Ch. 7.8 - Use a strip of paper and the folding procedure...Ch. 7.8 - Use the left-right rule to draw stage 2 of the...Ch. 7.8 - Use the left-right rule to determine the direction...Ch. 7.8 - Use the left-right rule to determine the direction...Ch. 7.8 - Use the left-right rule to determine the direction...Ch. 7.8 - Use an iterative process to draw stage 2 and stage...Ch. 7.8 - Use an iterative process to draw stage 2 and stage...Ch. 7.8 - Use an iterative process to draw stage 2 of the...Ch. 7.8 - Use an iterative process to draw stage 2 of the...Ch. 7.8 - Use an iterative process to draw stage 2 of the...Ch. 7.8 - Use an iterative process to draw stage 2 of the...Ch. 7.8 - Use an iterative process to draw stage 2 of the...Ch. 7.8 - Use an iterative process to draw stage 2 of the...Ch. 7.8 - Draw stage 3 and stage 4 of the fractal defined by...Ch. 7.8 - Draw stage 3 and stage 4 of the fractal defined by...Ch. 7.8 - Compute, if possible, the similarity dimension of...Ch. 7.8 - Compute, if possible, the similarity dimension of...Ch. 7.8 - Compute, if possible, the similarity dimension of...Ch. 7.8 - Compute, if possible, the similarity dimension of...Ch. 7.8 - Compute, if possible, the similarity dimension of...Ch. 7.8 - Compute, if possible, the similarity dimension of...Ch. 7.8 - Compute, if possible, the similarity dimension of...Ch. 7.8 - Compute, if possible, the similarity dimension of...Ch. 7.8 - Compute, if possible, the similarity dimension of...Ch. 7.8 - Compute, if possible, the similarity dimension of...Ch. 7.8 - Compare Similarity Dimensions Rank, from largest...Ch. 7.8 - The Peano Curve The Peano curve is defined by the...Ch. 7.8 - Explain why the similarity dimension formula...Ch. 7.8 - Stage 0 and stage 1 of Lévys curve (see Exercise...Ch. 7 - For Exercises 1 to 5, convert one measurement to...Ch. 7 - For Exercises 1 to 5, convert one measurement to...Ch. 7 - For Exercises 1 to 5, convert one measurement to...Ch. 7 - For Exercises 1 to 5, convert one measurement to...Ch. 7 - For Exercises 1 to 5, convert one measurement to...Ch. 7 - The price of a beverage is $3.56 per liter. What...Ch. 7 - Given that in ma=74 and in mb=52, find the...Ch. 7 - Triangles ABC and DEF are similar. Find the...Ch. 7 - Find the volume of the geometric solid.Ch. 7 - Find the measure of x.Ch. 7 - Find the surface area of the rectangular solid.Ch. 7 - The length of a diameter of the base of a cylinder...Ch. 7 - Given that BC=11 cm and that AB is three times the...Ch. 7 - Given that mx=150, find the measures of w and y.Ch. 7 - Find the area of a parallelogram that has a base...Ch. 7 - Find the volume of the square pyramid.Ch. 7 - Find the circumference of a circle that has a...Ch. 7 - Given that l1l2, find the measures of angles a and...Ch. 7 - Find the supplement of a 32° angle.Ch. 7 - Find the volume of a rectangular solid with a...Ch. 7 - Two angles of a triangle measure 37° and 48°....Ch. 7 - The height of a triangle is 7 cm. The area of the...Ch. 7 - Find the volume of a sphere that has a diameter of...Ch. 7 - Framing The perimeter of a square picture frame is...Ch. 7 - Paint A can of paint will cover 200 ft2 of...Ch. 7 - Parks and Recreation The length of a rectangular...Ch. 7 - Patios What is the area of a square patio that...Ch. 7 - Landscaping A walkway 2 m wide surrounds a...Ch. 7 - Determine whether the two triangles are congruent....Ch. 7 - Find the unknown side of the triangle. Round to...Ch. 7 - In Exercises 31 and 32, find the values of sin ,...Ch. 7 - In Exercises 31 and 32, find the values of sin ,...Ch. 7 - Use a calculator. Round to the nearest tenth of a...Ch. 7 - Use a calculator. Round to the nearest tenth of a...Ch. 7 - Use a calculator. Round to the nearest tenth of a...Ch. 7 - Use a calculator. Round to the nearest tenth of a...Ch. 7 - Surveying Find the distance across the marsh in...Ch. 7 - Angle of Depression The distance from a plane to a...Ch. 7 - Angle of Elevation The angle of elevation from a...Ch. 7 - What is another name for Riemannian geometry?Ch. 7 - What is another name for Lobachevskian geometry?Ch. 7 - Name a geometry in which the sum of the measures...Ch. 7 - Name a geometry in which there are no parallel...Ch. 7 - Determine the exact area of the spherical...Ch. 7 - Determine the exact area of the spherical...Ch. 7 - Euclidean and City Distances Find the Euclidean...Ch. 7 - Euclidean and City Distances Find the Euclidean...Ch. 7 - Euclidean and City Distances Find the Euclidean...Ch. 7 - Euclidean and City Distances Find the Euclidean...Ch. 7 - Consider the points P( 1, 1), Q(4, 5), and R(–4,...Ch. 7 - Draw stage 0, stage 1, and stage 2 of the Koch...Ch. 7 - Draw stage 2 of the fractal with the following...Ch. 7 - For the fractal defined in Exercise 52, determine...Ch. 7 - Compute the similarity dimension of a strictly...Ch. 7 - Find the volume of a cylinder with a height of 6 m...Ch. 7 - Find the perimeter of a rectangle that has a...Ch. 7 - Find the complement of a 32° angle.Ch. 7 - Find the area of a circle that has a diameter of 2...Ch. 7 - In the figure below, lines l1 and l2 are parallel....Ch. 7 - In the figure below, lines l1 and l2 are parallel....Ch. 7 - Convert: 1.2 m = ________ cm.Ch. 7 - Find the volume of the figure. Give the exact...Ch. 7 - Triangles ABC and DEF arc similar. Find side BC.Ch. 7 - A right triangle has a 40° angle. Find the...Ch. 7 - Find the measure of x.Ch. 7 - Find the area of the parallelogram shown below.Ch. 7 - Surveying Find the width of the canal shown in the...Ch. 7 - Pizza How much more area is in a pizza with radius...Ch. 7 - Determine whether the two triangles are congruent....Ch. 7 - For the right triangle shown below, determine the...Ch. 7 - Find the values of sin , cos , and tan for the...Ch. 7 - Angle of Elevation From a point 27 ft from the...Ch. 7 - Trees Find the cross-sectional area of a redwood...Ch. 7 - Toolbox A toolbox is 14 in. long, 9 in. wide, and...Ch. 7 - Find the speed, in meters per second, of a car...Ch. 7 - State the Euclidean parallel postulate.Ch. 7 - What is a great circle, and what formula is used...Ch. 7 - Find the area of a spherical triangle with a...Ch. 7 - City Geometry Find the Euclidean distance and the...Ch. 7 - City Geometry How many points are on the city...Ch. 7 - Draw stage 2 of the fractal with the given...Ch. 7 - Draw stage 2 of the fractal with the given...Ch. 7 - Compute the replacement ratio, scale ratio, and...Ch. 7 - Compute the replacement ratio, scale ratio, and...

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