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
Answer
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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
Answer
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
Answer
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.
Answered by 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.
Answered by 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
Answered by 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
Answered by 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.