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°
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°.
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
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°.
Sorry! please use the options giving as for that's not one of the options I listed.
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°.
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
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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.
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
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.