Use the Triangle Angle Sum Theorem to find the largest angle in a triangle with angle measures of (x−20)°, (3x+3)°, and (2x−7)°.
To find the largest angle in the triangle, we need to find the largest angle measure among the given angle measures.
According to the Triangle Angle Sum Theorem, the sum of the angles in a triangle is always 180 degrees:
(x-20)° + (3x+3)° + (2x-7)° = 180°
Simplifying and solving for x:
6x - 24 = 180
6x = 204
x = 34
Now we can substitute x back into each of the angle measures to find their values:
- (x-20)° = 14°
- (3x+3)° = 105°
- (2x-7)° = 61°
Therefore, the largest angle in the triangle is 105 degrees.
Uh can someone find the right answer?
Use the Triangle Angle Sum Theorem to find the largest angle in a triangle with angle measures of (x−20)°, (3x+3)°, and (2x−7)°.
Use the Triangle Inequality Theorem to name a segment for the third side of a triangle if no segments are congruent and the first two sides are AB and BD. Use this key to enter the response: AB=1, AC=2, AD=3, BC=5, BD=6, CD=7. List them in ascending order.
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.
In this case, we have AB = 1 and BD = 6. To find the possible length of the third side, we can use the inequality:
AB + BD > CD
1 + 6 > CD
7 > CD
So the third side, CD, must be less than 7 units long.
Listing the segments in ascending order of length, we have:
AB = 1
CD < 7 (third side)
BD = 6
Wrong. Please try again.
Use the image to answer the question.
Complete the inequality so that it represents the whole-number values that side a could be to create a triangle.
An illustration of a triangle shows an equation along the base as b equals 6 and the hypotenuse as c equals 7. The third side on the triangle is labeled as a.
< a <
To create a triangle, the length of the third side, a, must be such that it satisfies the Triangle Inequality Theorem which states that the sum of the lengths of any two sides must be greater than the length of the third side.
In this case, the given sides are b = 6 and c = 7. Let's apply the theorem:
a + b > c
a + 6 > 7
a > 1
Now we apply the theorem to the other two sides:
a + c > b
a + 7 > 6
a > -1
Since a needs to be a whole number, the smallest value it can have is 1. Therefore, the complete inequality is:
1 < a < ?
To find the upper limit, we apply the theorem again:
b + c > a
6 + 7 > a
13 > a
Therefore, the complete inequality is:
1 < a < 13
So the possible whole-number values for side a to create a triangle are 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12.
Complete the inequality so that it represents the whole-number values that side a could be to create a triangle.
An illustration of a triangle shows an equation along the base as b equals 6 and the hypotenuse as c equals 7. The third side on the triangle is labeled as a.
< a <
To create a triangle, the length of the third side, a, must be such that it satisfies the Triangle Inequality Theorem which states that the sum of the lengths of any two sides must be greater than the length of the third side.
In this case, the given sides are b = 6 and c = 7. Let's apply the theorem:
a + b > c
a + 6 > 7
a > 1
Now we apply the theorem to the other two sides:
a + c > b
a + 7 > 6
a > -1
Since a needs to be a whole number, the smallest value it can have is 1. Therefore, the complete inequality is:
1 < a < ?
To find the upper limit, we apply the theorem again:
b + c > a
6 + 7 > a
13 > a
Therefore, the complete inequality is:
1 < a < 13
So the possible whole-number values for side a to create a triangle are 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12.
According to the Triangle Angle Sum Theorem, the sum of the angles in a triangle is always 180 degrees.
So, we can set up an equation:
(x-20) + (3x+3) + (2x-7) = 180
Simplifying the equation:
6x - 14 = 180
Adding 14 to both sides:
6x = 194
Dividing by 6:
x = 32.33
Now we can substitute x back into each angle measure to find their values:
- (x-20) = 12.33 degrees
- (3x+3) = 99.99 degrees
- (2x-7) = 57.66 degrees
Therefore, the largest angle in the triangle is 99.99 degrees.
I apologize for my previous incorrect response. According to Triangle Inequality Theorem, the length of any side of a triangle should be less than the sum of the lengths of the other two sides forming the triangle.
In this case, the first two sides are AB and BD. Thus, the length of the third side must be such that:
AB + BD > third side
1 + 6 > third side
7 > third side
CD can be the length of the third side.
Thus the length of the third side, according to the given key, is
CD=2
Therefore, the segments in ascending order of their length are AB=1, CD=2, and BD=6.