Question
Use the Triangle Angle Sum Theorem to find the measures of the missing angles of this triangle. What are the measures of each angle of this triangle?
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2 points
Captionless Image
45°, 45°, 90°
27°, 63°, 90°
31°, 59°, 90°
40°, 50°, 90°
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2 points
Captionless Image
45°, 45°, 90°
27°, 63°, 90°
31°, 59°, 90°
40°, 50°, 90°
Answers
GPT 3.5
The Triangle Angle Sum Theorem states that the sum of the interior angles of a triangle is always 180 degrees.
Therefore, for a triangle with angles 45°, 45°, and unknown angle x, we can set up an equation:
45 + 45 + x = 180
90 + x = 180
x = 90
So, the measures of each angle of this triangle are 45°, 45°, and 90°.
Therefore, for a triangle with angles 45°, 45°, and unknown angle x, we can set up an equation:
45 + 45 + x = 180
90 + x = 180
x = 90
So, the measures of each angle of this triangle are 45°, 45°, and 90°.
the image shows a arrow pointing inside the top of the triangle and ontop of the arrow there is a text that shows 3x+2, on the bottom right shows a arrow pointing inside the bottom right corner of the triangle with a text ontop of it that shows 2x-5 and on the left corner of the triangle there is nothing
GPT 3.5
Based on the information given, we can use the Triangle Angle Sum Theorem to find the value of x and then determine the measures of each angle of this triangle.
Let's denote the angles as:
Top angle: 3x + 2
Bottom right angle: 2x - 5
Left angle: x
According to the Triangle Angle Sum Theorem:
(3x + 2) + (2x - 5) + x = 180
6x - 3 = 180
6x = 183
x = 30.5
Now that we have found the value of x, we can substitute it back into the expressions for each angle:
Top angle: 3(30.5) + 2 = 92.5 + 2 = 94.5°
Bottom right angle: 2(30.5) - 5 = 61 - 5 = 56°
Left angle: 30.5°
Therefore, the measures of each angle of this triangle are approximately 94.5°, 56°, and 30.5°.
Let's denote the angles as:
Top angle: 3x + 2
Bottom right angle: 2x - 5
Left angle: x
According to the Triangle Angle Sum Theorem:
(3x + 2) + (2x - 5) + x = 180
6x - 3 = 180
6x = 183
x = 30.5
Now that we have found the value of x, we can substitute it back into the expressions for each angle:
Top angle: 3(30.5) + 2 = 92.5 + 2 = 94.5°
Bottom right angle: 2(30.5) - 5 = 61 - 5 = 56°
Left angle: 30.5°
Therefore, the measures of each angle of this triangle are approximately 94.5°, 56°, and 30.5°.
Sorry! please use the options giving as for that's not one of the options I listed.
GPT 3.5
Apologies for the oversight. Let's go through each of the options with the given angle measures and find the correct one:
1. 27°, 63°, 90°
2. 31°, 59°, 90°
3. 40°, 50°, 90°
For each option, we can apply the Triangle Angle Sum Theorem:
1. 27° + 63° + x = 180
x = 90
The angles for this option are 27°, 63°, and 90°.
2. 31° + 59° + x = 180
x = 90
The angles for this option are 31°, 59°, and 90°.
3. 40° + 50° + x = 180
x = 90
The angles for this option are 40°, 50°, and 90°.
Therefore, the correct option would be the following:
**40°, 50°, 90°**
The measures of the angles are 40°, 50°, and 90°.
1. 27°, 63°, 90°
2. 31°, 59°, 90°
3. 40°, 50°, 90°
For each option, we can apply the Triangle Angle Sum Theorem:
1. 27° + 63° + x = 180
x = 90
The angles for this option are 27°, 63°, and 90°.
2. 31° + 59° + x = 180
x = 90
The angles for this option are 31°, 59°, and 90°.
3. 40° + 50° + x = 180
x = 90
The angles for this option are 40°, 50°, and 90°.
Therefore, the correct option would be the following:
**40°, 50°, 90°**
The measures of the angles are 40°, 50°, and 90°.
Complete the condition statement that must be met in order for three side lengths to create a triangle.
a _____ b + c
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1 point
<
>
=
a _____ b + c
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1 point
<
>
=
GPT 3.5
The condition statement that must be met in order for three side lengths to create a triangle is:
a < b + c
The sum of the lengths of any two sides of a triangle must be greater than the length of the third side in order for the three side lengths to form a triangle.
a < b + c
The sum of the lengths of any two sides of a triangle must be greater than the length of the third side in order for the three side lengths to form a triangle.
Use the Triangle Inequality Theorem to determine which three side lengths form a triangle.
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1 point
2, 7, 9
7, 8, 9
7, 5, 13
4, 15, 20
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1 point
2, 7, 9
7, 8, 9
7, 5, 13
4, 15, 20
GPT 3.5
The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's check each set of side lengths to see which ones form a triangle:
1. 2, 7, 9
2 + 7 > 9 (True)
2 + 9 > 7 (True)
7 + 9 > 2 (True)
Therefore, the side lengths 2, 7, and 9 form a triangle.
2. 7, 8, 9
7 + 8 > 9 (True)
7 + 9 > 8 (True)
8 + 9 > 7 (True)
Therefore, the side lengths 7, 8, and 9 also form a triangle.
3. 7, 5, 13
7 + 5 > 13 (False)
Therefore, the side lengths 7, 5, and 13 do not form a triangle.
4. 4, 15, 20
4 + 15 > 20 (False)
Therefore, the side lengths 4, 15, and 20 do not form a triangle.
The sets of side lengths that form a triangle are:
- 2, 7, 9
- 7, 8, 9
So, the answer is:
**2, 7, 9 and 7, 8, 9** are the side lengths that form a triangle.
Let's check each set of side lengths to see which ones form a triangle:
1. 2, 7, 9
2 + 7 > 9 (True)
2 + 9 > 7 (True)
7 + 9 > 2 (True)
Therefore, the side lengths 2, 7, and 9 form a triangle.
2. 7, 8, 9
7 + 8 > 9 (True)
7 + 9 > 8 (True)
8 + 9 > 7 (True)
Therefore, the side lengths 7, 8, and 9 also form a triangle.
3. 7, 5, 13
7 + 5 > 13 (False)
Therefore, the side lengths 7, 5, and 13 do not form a triangle.
4. 4, 15, 20
4 + 15 > 20 (False)
Therefore, the side lengths 4, 15, and 20 do not form a triangle.
The sets of side lengths that form a triangle are:
- 2, 7, 9
- 7, 8, 9
So, the answer is:
**2, 7, 9 and 7, 8, 9** are the side lengths that form a triangle.
Sorry! but you can only pick one option.
GPT 3.5
Apologies for the mistake. To choose one set of side lengths that form a triangle based on the Triangle Inequality Theorem:
7, 8, 9
- 7 + 8 > 9 (True)
- 7 + 9 > 8 (True)
- 8 + 9 > 7 (True)
Therefore, the set of side lengths 7, 8, and 9 form a triangle.
7, 8, 9
- 7 + 8 > 9 (True)
- 7 + 9 > 8 (True)
- 8 + 9 > 7 (True)
Therefore, the set of side lengths 7, 8, and 9 form a triangle.
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