Explanation Definition: Angles in a Triangle: “The sum of the measure of the angles in any triangle is 180 ∘ ”. It is symbolically written as ∠ A + ∠ B + ∠ C = 180 ∘ . Exterior angle: “An exterior angle of a triangle is the angle of the other side of an extension of one side of the triangle”. Sum of the exterior angle is 180 ∘ . Exterior angle property: “The measure of the exterior angle of a triangle equals to the sum of the measures of the two opposite interior angles”. Example: Consider the two interior angles 35 ∘ and 53 ∘ . The measure of the exterior angle x is found by adding the two interior angles. That is, 35 ∘ + 53 ∘ = x . This implies that x = 88 ∘ . Given: Assume that l 1 is parallel to l 2 . The angles of m ∠ 1 = 50 ∘ , m ∠ 9 = 40 ∘ . Calculation: From given triangle, it is observed that the measure of the angle is m ∠ 1 = 25 ∘ , m ∠ 20 = 105 ∘ . It is known that, if two lines are intersecting, then vertical angles are equal. Hence, m ∠ 3 = 25 ∘ . Here, l 1 is parallel to l 2 . Hence, m ∠ 20 = m ∠ 10 = m ∠ 12 = m ∠ 18 . That is, m ∠ 20 = m ∠ 10 = m ∠ 12 = m ∠ 18 = 105 ∘ . Compute m ∠ 6 by using the property of Exterior angle mentioned above. m ∠ 10 = m ∠ 3 + m ∠ 6 105 ∘ = 25 ∘ + m ∠ 6 m ∠ 6 = 105 ∘ − 25 ∘ m ∠ 6 = 80 ∘ Thus, m ∠ 6 = 80 ∘ . The vertical angles are equal. That is m ∠ 6 = m ∠ 8 . Thus, m ∠ 8 = 80 ∘ . Here, l 1 is parallel to l 2 . Thus, m ∠ 6 = m ∠ 8 = m ∠ 14 = m ∠ 16 = 80 ∘ . Consider the triangle Δ A B C , m ∠ 6 + m ∠ 9 + m ∠ 3 = 180 ∘ . Substitute m ∠ 3 = 25 ∘ and m ∠ 6 = 80 ∘ in m ∠ 6 + m ∠ 9 + m ∠ 3 = 180 ∘ . 80 ∘ + m ∠ 9 + 25 ∘ = 180 ∘ m ∠ 9 + 105 ∘ = 180 ∘ m ∠ 9 = 180 ∘ − 105 ∘ m ∠ 9 = 75 ∘ Thus, m ∠ 9 = 75 ∘

Nature of Mathematics (MindTap Course List)

13th Edition

ISBN: 9781133947257

Author: karl J. smith

Publisher: Cengage Learning

See similar textbooks

Concept explainers

Angles

In mathematics, angles constitute a very important part. Just like the concept of lines, an angle is a necessary figure that is used for measurement. How do you define its formation? It is formed when two or more lines meet at a point. The point at which…

Videos

Question

Chapter 7.3, Problem 30PS

To determine

To find:

The measure of all the angles of the given figure with m∠1=25∘, m∠20=105∘.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 7.3, Problem 29PS

Chapter 7.3, Problem 31PS

Students have asked these similar questions

Solve no chatgpt already got wrong chatgpt answer

Not use ai please

You may need to use the appropriate appendix table or technology to answer this question. You are given the following information obtained from a random sample of 4 observations. 24 48 31 57 You want to determine whether or not the mean of the population from which this sample was taken is significantly different from 49. (Assume the population is normally distributed.) (a) State the null and the alternative hypotheses. (Enter != for ≠ as needed.) H0: Ha: (b) Determine the test statistic. (Round your answer to three decimal places.) (c) Determine the p-value, and at the 5% level of significance, test to determine whether or not the mean of the population is significantly different from 49. Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. Reject H0. There is insufficient evidence to conclude that the mean of the population is different from 49.Do not reject H0. There is sufficient evidence to conclude that the…

Chapter 7 Solutions

Nature of Mathematics (MindTap Course List)

Ch. 7.1 - Is the woman in the figure a young woman or an old...Ch. 7.1 - Is the fly in the Figure 7.11 on the cube or in...Ch. 7.1 - Prob. 3PS Ch. 7.1 - Prob. 4PS Ch. 7.1 - Prob. 5PS Ch. 7.1 - Prob. 6PS Ch. 7.1 - Prob. 7PS Ch. 7.1 - Prob. 8PS Ch. 7.1 - Prob. 9PS Ch. 7.1 - Prob. 10PS

Ch. 7.1 - Prob. 11PS Ch. 7.1 - Prob. 12PS Ch. 7.1 - Prob. 13PS Ch. 7.1 - Prob. 14PS Ch. 7.1 - Prob. 15PS Ch. 7.1 - Prob. 16PS Ch. 7.1 - Prob. 17PS Ch. 7.1 - Prob. 18PS Ch. 7.1 - Use the illustration in Figure 7.12 to draw the...Ch. 7.1 - Prob. 20PS Ch. 7.1 - Prob. 21PS Ch. 7.1 - Prob. 22PS Ch. 7.1 - Prob. 23PS Ch. 7.1 - Prob. 24PS Ch. 7.1 - Prob. 25PS Ch. 7.1 - Prob. 26PS Ch. 7.1 - Prob. 27PS Ch. 7.1 - Carry out the constructions requested in Problems...Ch. 7.1 - Prob. 29PS Ch. 7.1 - Prob. 30PS Ch. 7.1 - Prob. 31PS Ch. 7.1 - Prob. 32PS Ch. 7.1 - Prob. 33PS Ch. 7.1 - Prob. 34PS Ch. 7.1 - Prob. 35PS Ch. 7.1 - Prob. 36PS Ch. 7.1 - Prob. 37PS Ch. 7.1 - Prob. 38PS Ch. 7.1 - Prob. 39PS Ch. 7.1 - Prob. 40PS Ch. 7.1 - Prob. 41PS Ch. 7.1 - Prob. 42PS Ch. 7.1 - Prob. 43PS Ch. 7.1 - Prob. 44PS Ch. 7.1 - Prob. 45PS Ch. 7.1 - Prob. 46PS Ch. 7.1 - Prob. 47PS Ch. 7.1 - Prob. 48PS Ch. 7.1 - Prob. 49PS Ch. 7.1 - Prob. 50PS Ch. 7.1 - Prob. 51PS Ch. 7.1 - Study the patterns shown in Figure 7.13. When...Ch. 7.1 - Prob. 53PS Ch. 7.1 - Prob. 54PS Ch. 7.1 - Prob. 55PS Ch. 7.1 - Prob. 56PS Ch. 7.1 - Prob. 57PS Ch. 7.1 - Prob. 58PS Ch. 7.1 - The letters of the alphabet can be sorted into the...Ch. 7.1 - Prob. 60PS Ch. 7.2 - Prob. 1PS Ch. 7.2 - Prob. 2PS Ch. 7.2 - Prob. 3PS Ch. 7.2 - Prob. 4PS Ch. 7.2 - Prob. 5PS Ch. 7.2 - Prob. 6PS Ch. 7.2 - Prob. 7PS Ch. 7.2 - Prob. 8PS Ch. 7.2 - Prob. 9PS Ch. 7.2 - Prob. 10PS Ch. 7.2 - Prob. 11PS Ch. 7.2 - Prob. 12PS Ch. 7.2 - Determine whether each sentence in Problems 11 14...Ch. 7.2 - Prob. 14PS Ch. 7.2 - Prob. 15PS Ch. 7.2 - Prob. 16PS Ch. 7.2 - Prob. 17PS Ch. 7.2 - Prob. 18PS Ch. 7.2 - Prob. 19PS Ch. 7.2 - Prob. 20PS Ch. 7.2 - Prob. 21PS Ch. 7.2 - Prob. 22PS Ch. 7.2 - Prob. 23PS Ch. 7.2 - Prob. 24PS Ch. 7.2 - In Problems 25 32, classify the pairs of angles...Ch. 7.2 - Prob. 26PS Ch. 7.2 - Prob. 27PS Ch. 7.2 - Prob. 28PS Ch. 7.2 - In Problems 25 32, classify the pairs of angles...Ch. 7.2 - Prob. 30PS Ch. 7.2 - Prob. 31PS Ch. 7.2 - Prob. 32PS Ch. 7.2 - Prob. 33PS Ch. 7.2 - Prob. 34PS Ch. 7.2 - Prob. 35PS Ch. 7.2 - Prob. 36PS Ch. 7.2 - Prob. 37PS Ch. 7.2 - Prob. 38PS Ch. 7.2 - Prob. 39PS Ch. 7.2 - Prob. 40PS Ch. 7.2 - Prob. 41PS Ch. 7.2 - Prob. 42PS Ch. 7.2 - Prob. 43PS Ch. 7.2 - Prob. 44PS Ch. 7.2 - Prob. 45PS Ch. 7.2 - Prob. 46PS Ch. 7.2 - Prob. 47PS Ch. 7.2 - Prob. 48PS Ch. 7.2 - Prob. 49PS Ch. 7.2 - Prob. 50PS Ch. 7.2 - Prob. 51PS Ch. 7.2 - In Problems 52 57, find the measures of all the...Ch. 7.2 - Prob. 53PS Ch. 7.2 - Prob. 54PS Ch. 7.2 - Prob. 55PS Ch. 7.2 - Prob. 56PS Ch. 7.2 - Prob. 57PS Ch. 7.2 - Prob. 58PS Ch. 7.2 - Prob. 59PS Ch. 7.2 - Historical Quest: Allow me to start you on a...Ch. 7.3 - IN YOUR OWN WORDS What is a triangle?Ch. 7.3 - Prob. 2PS Ch. 7.3 - IN YOUR OWN WORDS Explain the notation ABCDEF.Ch. 7.3 - Prob. 4PS Ch. 7.3 - Prob. 5PS Ch. 7.3 - Prob. 6PS Ch. 7.3 - Prob. 7PS Ch. 7.3 - Prob. 8PS Ch. 7.3 - Prob. 9PS Ch. 7.3 - Name the corresponding parts of the triangles in...Ch. 7.3 - In Problems 11-16, find the measure of the third...Ch. 7.3 - Prob. 12PS Ch. 7.3 - Prob. 13PS Ch. 7.3 - Prob. 14PS Ch. 7.3 - Prob. 15PS Ch. 7.3 - Prob. 16PS Ch. 7.3 - Prob. 17PS Ch. 7.3 - Prob. 18PS Ch. 7.3 - Prob. 19PS Ch. 7.3 - Prob. 20PS Ch. 7.3 - Prob. 21PS Ch. 7.3 - Prob. 22PS Ch. 7.3 - Prob. 23PS Ch. 7.3 - Prob. 24PS Ch. 7.3 - Prob. 25PS Ch. 7.3 - Prob. 26PS Ch. 7.3 - Prob. 27PS Ch. 7.3 - Prob. 28PS Ch. 7.3 - Prob. 29PS Ch. 7.3 - Prob. 30PS Ch. 7.3 - Prob. 31PS Ch. 7.3 - Prob. 32PS Ch. 7.3 - Prob. 33PS Ch. 7.3 - Prob. 34PS Ch. 7.3 - Use algebra to find the value of x in each of the...Ch. 7.3 - Prob. 36PS Ch. 7.3 - Prob. 37PS Ch. 7.3 - Use algebra to find the value of x in each of the...Ch. 7.3 - Prob. 39PS Ch. 7.3 - Prob. 40PS Ch. 7.3 - Prob. 41PS Ch. 7.3 - Prob. 42PS Ch. 7.3 - Prob. 43PS Ch. 7.3 - Prob. 44PS Ch. 7.3 - Prob. 45PS Ch. 7.3 - Prob. 46PS Ch. 7.3 - Prob. 47PS Ch. 7.3 - Prob. 48PS Ch. 7.3 - Prob. 49PS Ch. 7.3 - Prob. 50PS Ch. 7.3 - Prob. 51PS Ch. 7.3 - Prob. 52PS Ch. 7.3 - Prob. 53PS Ch. 7.3 - Prob. 54PS Ch. 7.3 - Prob. 55PS Ch. 7.3 - Prob. 56PS Ch. 7.3 - The legs of a picnic table form a triangle where...Ch. 7.3 - Prob. 58PS Ch. 7.3 - Prob. 59PS Ch. 7.3 - Prob. 60PS Ch. 7.4 - IN YOUR OWN WORDS Contrast congruent and similar...Ch. 7.4 - Prob. 2PS Ch. 7.4 - In Problems 3-8, determine if the triangles are...Ch. 7.4 - Prob. 4PS Ch. 7.4 - Prob. 5PS Ch. 7.4 - Prob. 6PS Ch. 7.4 - Prob. 7PS Ch. 7.4 - Prob. 8PS Ch. 7.4 - Prob. 9PS Ch. 7.4 - Prob. 10PS Ch. 7.4 - Prob. 11PS Ch. 7.4 - Prob. 12PS Ch. 7.4 - Prob. 13PS Ch. 7.4 - Prob. 14PS Ch. 7.4 - Prob. 15PS Ch. 7.4 - Prob. 16PS Ch. 7.4 - Prob. 17PS Ch. 7.4 - Prob. 18PS Ch. 7.4 - Prob. 19PS Ch. 7.4 - Prob. 20PS Ch. 7.4 - Prob. 21PS Ch. 7.4 - Prob. 22PS Ch. 7.4 - Prob. 23PS Ch. 7.4 - Prob. 24PS Ch. 7.4 - Prob. 25PS Ch. 7.4 - Prob. 26PS Ch. 7.4 - Prob. 27PS Ch. 7.4 - Prob. 28PS Ch. 7.4 - Prob. 29PS Ch. 7.4 - Each figure in Problems 29-34 contains two similar...Ch. 7.4 - Prob. 31PS Ch. 7.4 - Prob. 32PS Ch. 7.4 - Prob. 33PS Ch. 7.4 - Prob. 34PS Ch. 7.4 - Prob. 35PS Ch. 7.4 - Prob. 36PS Ch. 7.4 - Given AC is perpendicular to MB, and ABC is an...Ch. 7.4 - Prob. 38PS Ch. 7.4 - Prob. 39PS Ch. 7.4 - Prob. 40PS Ch. 7.4 - Use similar triangles and a proportion to find the...Ch. 7.4 - Prob. 42PS Ch. 7.4 - Prob. 43PS Ch. 7.4 - Prob. 44PS Ch. 7.4 - Prob. 45PS Ch. 7.4 - Prob. 46PS Ch. 7.4 - A bell tower casts a shadow 45ft long. At the same...Ch. 7.4 - Prob. 48PS Ch. 7.4 - Prob. 49PS Ch. 7.4 - Prob. 50PS Ch. 7.4 - Prob. 51PS Ch. 7.4 - Prob. 52PS Ch. 7.4 - Prob. 53PS Ch. 7.4 - Prob. 54PS Ch. 7.4 - Prob. 55PS Ch. 7.4 - Suppose a 6- ft person wishes to determine the...Ch. 7.4 - Prob. 57PS Ch. 7.4 - Prob. 58PS Ch. 7.4 - Prob. 59PS Ch. 7.4 - Prob. 60PS Ch. 7.5 - Prob. 1PS Ch. 7.5 - Prob. 2PS Ch. 7.5 - Prob. 3PS Ch. 7.5 - Prob. 4PS Ch. 7.5 - Prob. 5PS Ch. 7.5 - Prob. 6PS Ch. 7.5 - Prob. 7PS Ch. 7.5 - Prob. 8PS Ch. 7.5 - Prob. 9PS Ch. 7.5 - Prob. 10PS Ch. 7.5 - Prob. 11PS Ch. 7.5 - Prob. 12PS Ch. 7.5 - Prob. 13PS Ch. 7.5 - Prob. 14PS Ch. 7.5 - Prob. 15PS Ch. 7.5 - Prob. 16PS Ch. 7.5 - Prob. 17PS Ch. 7.5 - Prob. 18PS Ch. 7.5 - Prob. 19PS Ch. 7.5 - Prob. 20PS Ch. 7.5 - Prob. 21PS Ch. 7.5 - Prob. 22PS Ch. 7.5 - Prob. 23PS Ch. 7.5 - Prob. 24PS Ch. 7.5 - Prob. 25PS Ch. 7.5 - Prob. 26PS Ch. 7.5 - Prob. 27PS Ch. 7.5 - Prob. 28PS Ch. 7.5 - Prob. 29PS Ch. 7.5 - Prob. 30PS Ch. 7.5 - Prob. 31PS Ch. 7.5 - Prob. 32PS Ch. 7.5 - Prob. 33PS Ch. 7.5 - Prob. 34PS Ch. 7.5 - Prob. 35PS Ch. 7.5 - Prob. 36PS Ch. 7.5 - Prob. 37PS Ch. 7.5 - Prob. 38PS Ch. 7.5 - Prob. 39PS Ch. 7.5 - Prob. 40PS Ch. 7.5 - Prob. 41PS Ch. 7.5 - Prob. 42PS Ch. 7.5 - Prob. 43PS Ch. 7.5 - Prob. 44PS Ch. 7.5 - Prob. 45PS Ch. 7.5 - Prob. 46PS Ch. 7.5 - Prob. 47PS Ch. 7.5 - Level 2 If the angle from the horizontal to the...Ch. 7.5 - Prob. 49PS Ch. 7.5 - Prob. 50PS Ch. 7.5 - Prob. 51PS Ch. 7.5 - Prob. 52PS Ch. 7.5 - Prob. 53PS Ch. 7.5 - Prob. 54PS Ch. 7.5 - Prob. 55PS Ch. 7.5 - Prob. 56PS Ch. 7.5 - Prob. 57PS Ch. 7.5 - Prob. 58PS Ch. 7.5 - Prob. 59PS Ch. 7.5 - Problem solving Level 3 a. If the distance from...Ch. 7.6 - Prob. 1PS Ch. 7.6 - Prob. 2PS Ch. 7.6 - Prob. 3PS Ch. 7.6 - Prob. 4PS Ch. 7.6 - Prob. 5PS Ch. 7.6 - Prob. 6PS Ch. 7.6 - Prob. 7PS Ch. 7.6 - Prob. 8PS Ch. 7.6 - Prob. 9PS Ch. 7.6 - Prob. 10PS Ch. 7.6 - Prob. 11PS Ch. 7.6 - Prob. 12PS Ch. 7.6 - Name the geometry Euclidean, elliptic, or...Ch. 7.6 - Prob. 14PS Ch. 7.6 - Prob. 15PS Ch. 7.6 - Prob. 16PS Ch. 7.6 - Prob. 17PS Ch. 7.6 - Prob. 18PS Ch. 7.6 - Prob. 19PS Ch. 7.6 - Prob. 20PS Ch. 7.6 - Prob. 21PS Ch. 7.6 - Prob. 22PS Ch. 7.6 - Prob. 23PS Ch. 7.6 - Prob. 24PS Ch. 7.6 - Prob. 25PS Ch. 7.6 - Prob. 26PS Ch. 7.6 - Prob. 27PS Ch. 7.6 - Prob. 28PS Ch. 7.6 - Consider the top, front, and side views as shown...Ch. 7.6 - Prob. 30PS Ch. 7.6 - Prob. 31PS Ch. 7.6 - Prob. 32PS Ch. 7.6 - Prob. 33PS Ch. 7.6 - Prob. 34PS Ch. 7.6 - Prob. 35PS Ch. 7.6 - Prob. 36PS Ch. 7.6 - Prob. 37PS Ch. 7.6 - Prob. 38PS Ch. 7.6 - Prob. 39PS Ch. 7.6 - Prob. 40PS Ch. 7.6 - Prob. 41PS Ch. 7.6 - Prob. 42PS Ch. 7.6 - Prob. 43PS Ch. 7.6 - Prob. 44PS Ch. 7.6 - Prob. 45PS Ch. 7.6 - Prob. 46PS Ch. 7.6 - Prob. 47PS Ch. 7.6 - Prob. 48PS Ch. 7.6 - Prob. 49PS Ch. 7.6 - Prob. 50PS Ch. 7.6 - Prob. 51PS Ch. 7.6 - Prob. 52PS Ch. 7.6 - Prob. 53PS Ch. 7.6 - Prob. 54PS Ch. 7.6 - When is an open book a closed book? If the...Ch. 7.6 - Prob. 56PS Ch. 7.6 - Prob. 57PS Ch. 7.6 - Prob. 58PS Ch. 7.6 - Prob. 59PS Ch. 7.CR - Prob. 1CR Ch. 7.CR - Prob. 2CR Ch. 7.CR - Prob. 3CR Ch. 7.CR - Prob. 4CR Ch. 7.CR - Prob. 5CR Ch. 7.CR - Prob. 6CR Ch. 7.CR - 7. Bourbon Palace Figure 7.77 is home to the...Ch. 7.CR - Prob. 8CR Ch. 7.CR - Prob. 9CR Ch. 7.CR - Prob. 10CR Ch. 7.CR - Prob. 11CR Ch. 7.CR - Prob. 12CR Ch. 7.CR - Prob. 13CR Ch. 7.CR - Prob. 14CR Ch. 7.CR - Prob. 15CR Ch. 7.CR - Prob. 16CR Ch. 7.CR - Prob. 17CR Ch. 7.CR - Prob. 18CR Ch. 7.CR - Prob. 19CR Ch. 7.CR - Prob. 20CR

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

The measure of all the angles of the given figure with m ∠ 1 = 25 ∘ , m ∠ 20 = 105 ∘ .

Solution Summary: The author explains the measure of all the angles of the given figure with mangle 1=25circ .

Concept explainers

Videos

To find:

The measure of all the angles of the given figure with m∠1=25∘, m∠20=105∘.

Want to see the full answer?

Chapter 7 Solutions

The measure of all the angles of the given figure with m ∠ 1 = 25 ∘ , m ∠ 20 = 105 ∘ .

Solution Summary: The author explains the measure of all the angles of the given figure with mangle 1=25circ .

Concept explainers

Videos

To find: The measure of all the angles of the given figure with m∠1=25∘, m∠20=105∘.

Want to see the full answer?

Chapter 7 Solutions

To find:

The measure of all the angles of the given figure with m∠1=25∘, m∠20=105∘.