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 = 50 ∘ , m ∠ 9 = 40 ∘ . It is known that, if two lines are intersecting, then vertical angles are equal. Hence, m ∠ 3 = 50 ∘ and m ∠ 11 = 40 ∘ . Consider the triangle Δ A B C , m ∠ 6 + m ∠ 9 + m ∠ 3 = 180 ∘ . Substitute m ∠ 3 = 50 ∘ and m ∠ 9 = 40 ∘ in m ∠ 6 + m ∠ 9 + m ∠ 3 = 180 ∘ . m ∠ 6 + 40 ∘ + 50 ∘ = 180 ∘ m ∠ 6 + 90 ∘ = 180 ∘ m ∠ 6 = 180 ∘ − 90 ∘ m ∠ 6 = 90 ∘ Thus, m ∠ 6 = 90 ∘ . The vertical angles are equal. That is m ∠ 6 = m ∠ 8 . Thus, m ∠ 8 = 90 ∘ . Compute m ∠ 4 by using the property of Exterior angle mentioned above. m ∠ 4 = m ∠ 9 + m ∠ 6 m ∠ 4 = 40 ∘ + 90 ∘ = 130 ∘ Thus, m ∠ 4 = 130 ∘ . The vertical angles are equal. That is m ∠ 4 = m ∠ 2 . Thus, m ∠ 2 = 130 ∘ . Compute m ∠ 10 by using the property of Exterior angle mentioned above. m ∠ 10 = m ∠ 3 + m ∠ 6 m ∠ 10 = 50 ∘ + 90 ∘ = 140 ∘ Thus, m ∠ 10 = 140 ∘

Nature of Mathematics (MindTap Course List)

13th Edition

ISBN: 9781133947257

Author: karl J. smith

Publisher: Cengage Learning

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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…

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Chapter 7.3, Problem 29PS

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The measure of all the angles of the given figure with m∠1=50∘, m∠9=40∘.

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Chapter 7.3, Problem 28PS

Chapter 7.3, Problem 30PS

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The measure of all the angles of the given figure with m ∠ 1 = 50 ∘ , m ∠ 9 = 40 ∘ .

Solution Summary: The author explains the measure of all the angles of the given figure with mangle 1=50circ .

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The measure of all the angles of the given figure with m∠1=50∘, m∠9=40∘.

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Chapter 7 Solutions

The measure of all the angles of the given figure with m ∠ 1 = 50 ∘ , m ∠ 9 = 40 ∘ .

Solution Summary: The author explains the measure of all the angles of the given figure with mangle 1=50circ .

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To find: The measure of all the angles of the given figure with m∠1=50∘, m∠9=40∘.

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Chapter 7 Solutions

To find:

The measure of all the angles of the given figure with m∠1=50∘, m∠9=40∘.