4.1 & 4.2 Triangles, Interior And Exterior

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

5x = 120 + x

120 + x + 5x = 180

120 + x = 5x + 180

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.

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.

2) What is the value of x for the picture below?

6.75

15

27

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Explanation

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3) What is the value of x?

40

45

50

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

Explanation

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

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

16.6

19.3

22

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.

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.

5)

80

50

40

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Explanation

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6) What is the value for x in the picture below?

60

75

105

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Explanation

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

180

360

Not enough information

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.

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.

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

90

180

360

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.

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.

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

The length of each side is 20.

The length of each side is 40.

The length of each side is 60.

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.

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.

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

Right Obtuse

Isosceles Obtuse

Scalene Obtuse

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.

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.

11)

90

100

126

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.

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.