Question
The angle measures of a triangle are shown in the diagram.
What is the value of x?
*
2 points
A. 55
B. 21
C. 11
D. 28
the angles are (5x) degrees (4x+7) degrees and 74 degrees
What is the value of x?
*
2 points
A. 55
B. 21
C. 11
D. 28
the angles are (5x) degrees (4x+7) degrees and 74 degrees
Answers
GPT 3.5
To find the value of x, we can use the fact that the sum of angles in a triangle is always 180 degrees.
So, we have (5x) + (4x + 7) + 74 = 180.
Combine like terms: 9x + 7 + 74 = 180.
Combine constants: 9x + 81 = 180.
Subtract 81 from both sides: 9x = 99.
Divide both sides by 9: x = 11.
Therefore, the value of x is 11.
The answer is C. 11.
So, we have (5x) + (4x + 7) + 74 = 180.
Combine like terms: 9x + 7 + 74 = 180.
Combine constants: 9x + 81 = 180.
Subtract 81 from both sides: 9x = 99.
Divide both sides by 9: x = 11.
Therefore, the value of x is 11.
The answer is C. 11.
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The measure of one angle in a triangle is 2x degrees, the second angle is 3x + 10 degrees, and the third angle is 4x - 19 degrees. Find the value of x and the measures of all three angles.
enter just the numbers with a space in between and no commas
The measure of one angle in a triangle is 2x degrees, the second angle is 3x + 10 degrees, and the third angle is 4x - 19 degrees. Find the value of x and the measures of all three angles.
enter just the numbers with a space in between and no commas
GPT 3.5
To find the value of x and the measures of all three angles, we can use the fact that the sum of angles in a triangle is always 180 degrees.
So, we have 2x + (3x + 10) + (4x - 19) = 180.
Combine like terms: 9x - 9 = 180.
Add 9 to both sides: 9x = 189.
Divide both sides by 9: x = 21.
Now we can substitute the value of x back into the expressions for the angles:
Angle 1: 2x = 2(21) = 42 degrees
Angle 2: 3x + 10 = 3(21) + 10 = 73 degrees
Angle 3: 4x - 19 = 4(21) - 19 = 85 degrees
Therefore, the value of x is 21 and the measures of the three angles are 42 degrees, 73 degrees, and 85 degrees.
42 73 85
So, we have 2x + (3x + 10) + (4x - 19) = 180.
Combine like terms: 9x - 9 = 180.
Add 9 to both sides: 9x = 189.
Divide both sides by 9: x = 21.
Now we can substitute the value of x back into the expressions for the angles:
Angle 1: 2x = 2(21) = 42 degrees
Angle 2: 3x + 10 = 3(21) + 10 = 73 degrees
Angle 3: 4x - 19 = 4(21) - 19 = 85 degrees
Therefore, the value of x is 21 and the measures of the three angles are 42 degrees, 73 degrees, and 85 degrees.
42 73 85
The measure of one angle in a triangle is 8c + 10 degrees, the second angle is 3c - 20 degrees, and the third angle is 5c + 30 degrees. Find the value of c and the measures of all three angles.
enter just the numbers with a space in between and no commas
enter just the numbers with a space in between and no commas
GPT 3.5
To find the value of c and the measures of all three angles, we can use the fact that the sum of angles in a triangle is always 180 degrees.
So, we have 8c + 10 + (3c - 20) + (5c + 30) = 180.
Combine like terms: 16c + 20 = 180.
Subtract 20 from both sides: 16c = 160.
Divide both sides by 16: c = 10.
Now we can substitute the value of c back into the expressions for the angles:
Angle 1: 8c + 10 = 8(10) + 10 = 90 degrees
Angle 2: 3c - 20 = 3(10) - 20 = 10 degrees
Angle 3: 5c + 30 = 5(10) + 30 = 80 degrees
Therefore, the value of c is 10 and the measures of the three angles are 90 degrees, 10 degrees, and 80 degrees.
90 10 80
So, we have 8c + 10 + (3c - 20) + (5c + 30) = 180.
Combine like terms: 16c + 20 = 180.
Subtract 20 from both sides: 16c = 160.
Divide both sides by 16: c = 10.
Now we can substitute the value of c back into the expressions for the angles:
Angle 1: 8c + 10 = 8(10) + 10 = 90 degrees
Angle 2: 3c - 20 = 3(10) - 20 = 10 degrees
Angle 3: 5c + 30 = 5(10) + 30 = 80 degrees
Therefore, the value of c is 10 and the measures of the three angles are 90 degrees, 10 degrees, and 80 degrees.
90 10 80
Given Information: 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 other words, if a, b, and c are the lengths of the sides of a triangle, then the following conditions must hold true:
a + b > c
a + c > b
b + c > a
Question:
1. True or False: The segments of lengths 5, 7, and 10 can form a triangle.
a + b > c
a + c > b
b + c > a
Question:
1. True or False: The segments of lengths 5, 7, and 10 can form a triangle.
GPT 3.5
To determine if the segments of lengths 5, 7, and 10 can form a triangle, we need to check if the triangle inequality holds true for these lengths.
Using the triangle inequality theorem:
5 + 7 > 10
7 + 10 > 5
5 + 10 > 7
Simplifying each equation:
12 > 10
17 > 5
15 > 7
Since all three conditions hold true, the segments of lengths 5, 7, and 10 can form a triangle.
Therefore, the statement is true: The segments of lengths 5, 7, and 10 can form a triangle.
Using the triangle inequality theorem:
5 + 7 > 10
7 + 10 > 5
5 + 10 > 7
Simplifying each equation:
12 > 10
17 > 5
15 > 7
Since all three conditions hold true, the segments of lengths 5, 7, and 10 can form a triangle.
Therefore, the statement is true: The segments of lengths 5, 7, and 10 can form a triangle.