Question
The ___ of all __ angles in triangle is ___ degrees
Answers
Answer
Two angles in a triangles measure 34 degrees and 101 degrees. What is the measure of the third angle
A.32
B. 39
C. 45
D.54
A.32
B. 39
C. 45
D.54
Answer
Identify the combination of angle measures the could from a triangle
A. 30,75, 85
B. 25, 65, 90
C. 45,65, 75
D.40, 55 ,95
A. 30,75, 85
B. 25, 65, 90
C. 45,65, 75
D.40, 55 ,95
Answer
The angles of a triangle measure 2x, 3x, and 4x. Using the triangle angle sum theorem, find the measure of the smallest angle in this triangle
Answer
Two sides of the a triangle are 10 mm and 7 mm. Using the Triangle Inequality Theorem, determine the the length of the third side from the choices given
A. 5 mm
B. 2 mm
C. 1 mm
D. 20 mm
A. 5 mm
B. 2 mm
C. 1 mm
D. 20 mm
Answer
Apply the triangle Inequality Theorem to determine which three side lengths from a triangle
A. 8,4, 12
B. 20,10, 30
C. 10, 20, 30
D.8, 8, 20
A. 8,4, 12
B. 20,10, 30
C. 10, 20, 30
D.8, 8, 20
Answered by
GPT 3.5
The sum of all interior angles in a triangle is 180 degrees.
Answered by
GPT 3.5
To find the measure of the third angle in the triangle, you need to subtract the sum of the other two angles from 180 degrees.
Let's designate the third angle as x.
34 degrees + 101 degrees + x = 180 degrees
Combine like terms:
135 degrees + x = 180 degrees
Now, isolate x by subtracting 135 degrees from both sides:
x = 180 degrees - 135 degrees
x = 45 degrees
Therefore, the measure of the third angle is 45 degrees. Thus, the correct answer is C. 45.
Let's designate the third angle as x.
34 degrees + 101 degrees + x = 180 degrees
Combine like terms:
135 degrees + x = 180 degrees
Now, isolate x by subtracting 135 degrees from both sides:
x = 180 degrees - 135 degrees
x = 45 degrees
Therefore, the measure of the third angle is 45 degrees. Thus, the correct answer is C. 45.
Answered by
GPT 3.5
In order for a triangle to be formed, the sum of the measures of the three angles must equal 180 degrees.
Let's check each option:
A. 30 + 75 + 85 = 190 (not equal to 180)
B. 25 + 65 + 90 = 180 (equal to 180)
C. 45 + 65 + 75 = 185 (not equal to 180)
D. 40 + 55 + 95 = 190 (not equal to 180)
Only option B, 25, 65, 90, has angle measures that add up to 180 degrees. Therefore, the correct answer is B. 25, 65, 90.
Let's check each option:
A. 30 + 75 + 85 = 190 (not equal to 180)
B. 25 + 65 + 90 = 180 (equal to 180)
C. 45 + 65 + 75 = 185 (not equal to 180)
D. 40 + 55 + 95 = 190 (not equal to 180)
Only option B, 25, 65, 90, has angle measures that add up to 180 degrees. Therefore, the correct answer is B. 25, 65, 90.
Answered by
GPT 3.5
According to the triangle angle sum theorem, the sum of the measures of the angles in a triangle is always 180 degrees.
Let's denote the measures of the angles as 2x, 3x, and 4x.
We can now set up the equation:
2x + 3x + 4x = 180
Combine like terms:
9x = 180
Now, solve for x by dividing both sides of the equation by 9:
x = 180 / 9
x = 20
To find the measure of the smallest angle, substitute x back into the expression 2x:
2(20) = 40
Therefore, the measure of the smallest angle in this triangle is 40 degrees.
Let's denote the measures of the angles as 2x, 3x, and 4x.
We can now set up the equation:
2x + 3x + 4x = 180
Combine like terms:
9x = 180
Now, solve for x by dividing both sides of the equation by 9:
x = 180 / 9
x = 20
To find the measure of the smallest angle, substitute x back into the expression 2x:
2(20) = 40
Therefore, the measure of the smallest angle in this triangle is 40 degrees.
Answered by
GPT 3.5
According to the Triangle Inequality Theorem, in a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Let's check the options:
A. 10 mm + 7 mm = 17 mm (greater than 5 mm) - Not a possible length for the third side
B. 10 mm + 7 mm = 17 mm (greater than 2 mm) - Not a possible length for the third side
C. 10 mm + 7 mm = 17 mm (greater than 1 mm) - Not a possible length for the third side
D. 10 mm + 7 mm = 17 mm (not greater than 20 mm) - A possible length for the third side
Therefore, the length of the third side from the given choices is 20 mm, so the correct answer is D. 20 mm.
Let's check the options:
A. 10 mm + 7 mm = 17 mm (greater than 5 mm) - Not a possible length for the third side
B. 10 mm + 7 mm = 17 mm (greater than 2 mm) - Not a possible length for the third side
C. 10 mm + 7 mm = 17 mm (greater than 1 mm) - Not a possible length for the third side
D. 10 mm + 7 mm = 17 mm (not greater than 20 mm) - A possible length for the third side
Therefore, the length of the third side from the given choices is 20 mm, so the correct answer is D. 20 mm.
Answered by
GPT 3.5
According to the Triangle Inequality Theorem, in a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Let's check each option:
A. 8 + 4 = 12 (equal to 12, not greater than 12) - Not valid
B. 20 + 10 = 30 (equal to 30, not greater than 30) - Not valid
C. 10 + 20 = 30 (greater than 30) - Not valid
D. 8 + 8 = 16 (greater than 20) - Not valid
None of the options satisfy the Triangle Inequality Theorem. Therefore, there are no valid combinations of side lengths to form a triangle among the given options.
Let's check each option:
A. 8 + 4 = 12 (equal to 12, not greater than 12) - Not valid
B. 20 + 10 = 30 (equal to 30, not greater than 30) - Not valid
C. 10 + 20 = 30 (greater than 30) - Not valid
D. 8 + 8 = 16 (greater than 20) - Not valid
None of the options satisfy the Triangle Inequality Theorem. Therefore, there are no valid combinations of side lengths to form a triangle among the given options.