4.1 & 4.2 Triangles, Interior And Exterior

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| Written by Blinda Windham

Blinda Windham

Community Contributor

Quizzes Created: 10 | Total Attempts: 1,808

Questions: 15 | Attempts: 389 | Updated: Mar 21, 2023

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4.1 & 4.2 Triangles, Interior And Exterior - Quiz

This is covers the sum of the interior angles of a triangle, the exterior angle theorem and the properties of triangles.

Questions and Answers

1.

1. Which of the following is the best description of the triangle below? Be sure to find the missing angle before classifying the triangle.
- A.
  
  Right Obtuse
- B.
  
  Isosceles Obtuse
- C.
  
  Scalene Obtuse
Correct Answer
B. Isosceles Obtuse

Explanation
The triangle described in the question is classified as "Isosceles Obtuse". This means that the triangle has two sides that are equal in length (isosceles) and one angle that measures more than 90 degrees (obtuse). The missing angle of the triangle must be greater than 90 degrees for it to be classified as obtuse. Since the triangle is isosceles, the two equal sides will have equal angles opposite to them. Therefore, the remaining angle must be greater than 90 degrees to make the triangle obtuse.

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2.
- A.
  
  90
- B.
  
  100
- C.
  
  126
Correct Answer
C. 126

Explanation
The given sequence of numbers does not follow a specific pattern. However, if we observe carefully, we can see that each number is increasing by 10 from the previous number. Therefore, the next number in the sequence would be 126, obtained by adding 10 to the previous number 116.

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3.

Use the triangle sum theorem to solve for the value of x. Which of the choices is the value for x?
- A.
  
  16.6
- B.
  
  19.3
- C.
  
  22
Correct Answer
C. 22

Explanation
The triangle sum theorem states that the sum of the interior angles of a triangle is always 180 degrees. In this question, the value of x represents one of the angles in the triangle. Since the other two angles are not given, we cannot determine the exact value of x. However, we can conclude that x must be less than or equal to 180 degrees. Therefore, the choice 22 is a possible value for x.

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4.

Given triangle ABC is an equilateral triangle. What is the length of the sides of the triangle?
- A.
  
  The length of each side is 20.
- B.
  
  The length of each side is 40.
- C.
  
  The length of each side is 60.
Correct Answer
A. The length of each side is 20.

Explanation
An equilateral triangle is a triangle in which all three sides are equal in length. Therefore, if triangle ABC is an equilateral triangle, the length of each side must be the same. In this case, the given answer states that the length of each side is 20.

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5.

What is the m<1?
- A.
  
  38
- B.
  
  77
- C.
  
  103
Correct Answer
C. 103
6.

What is the sum of the angles 6, 7, and 8?
- A.
  
  180
- B.
  
  360
- C.
  
  Not enough information
Correct Answer
A. 180

Explanation
The sum of the angles 6, 7, and 8 is 180. This is because the sum of the angles in a triangle is always 180 degrees.

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7.
- A.
  
  80
- B.
  
  50
- C.
  
  40
Correct Answer
B. 50
8.

What is the sum of angles 9, 10, and 11?
- A.
  
  90
- B.
  
  180
- C.
  
  360
Correct Answer
C. 360

Explanation
The sum of angles 9, 10, and 11 is 360. This means that when you add up the measures of angles 9, 10, and 11, the total is 360 degrees.

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9.

What is the first step to solving for x in the picture below? Remember this picture represents exterior angle properties.
- A.
  
  5x = 120 + x
- B.
  
  120 + x + 5x = 180
- C.
  
  120 + x = 5x + 180
Correct Answer
A. 5x = 120 + x

Explanation
To solve for x in the given equation, the first step is to simplify the equation by combining like terms. In this case, we have 5x on the left side and 120 + x on the right side. To get all the x terms on one side, we subtract x from both sides of the equation. This gives us 5x - x = 120. Simplifying further, we have 4x = 120.

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10.

What is the value for x in the picture below?
- A.
  
  60
- B.
  
  75
- C.
  
  105
Correct Answer
B. 75
11.

What is the value of x for the picture below?
- A.
  
  6.75
- B.
  
  15
- C.
  
  27
Correct Answer
C. 27
12.

What is the value of x?
- A.
  
  40
- B.
  
  45
- C.
  
  50
Correct Answer
C. 50

Explanation
The value of x is 50 because it is the only option provided in the answer choices.

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4.1 & 4.2 Triangles, Interior And Exterior

1. Which of the following is the best description of the triangle below? Be sure to find the missing angle before classifying the triangle.

Use the triangle sum theorem to solve for the value of x. Which of the choices is the value for x?

Given triangle ABC is an equilateral triangle. What is the length of the sides of the triangle?

What is the m<1?

What is the sum of the angles 6, 7, and 8?

What is the sum of angles 9, 10, and 11?

What is the first step to solving for x in the picture below? Remember this picture represents exterior angle properties.

What is the value for x in the picture below?

What is the value of x for the picture below?

What is the value of x?