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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.
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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.
*This question will be teacher graded*
*
2 points
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just replace therefore with so
and we with I
and we with I
Answered by
GPT 3.5
To find the value of x and the measures of all three angles, we need to use the fact that the sum of all angles in a triangle is always 180 degrees.
Let's set up an equation based on this information:
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 that we have found the value of x, we can substitute it into the expressions for each angle to find their measures:
First angle: 2x = 2(21) = 42 degrees
Second angle: 3x + 10 = 3(21) + 10 = 63 + 10 = 73 degrees
Third angle: 4x - 19 = 4(21) - 19 = 84 - 19 = 65 degrees
Therefore, the value of x is 21, and the measures of the three angles are 42 degrees, 73 degrees, and 65 degrees.
Let's set up an equation based on this information:
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 that we have found the value of x, we can substitute it into the expressions for each angle to find their measures:
First angle: 2x = 2(21) = 42 degrees
Second angle: 3x + 10 = 3(21) + 10 = 63 + 10 = 73 degrees
Third angle: 4x - 19 = 4(21) - 19 = 84 - 19 = 65 degrees
Therefore, the value of x is 21, and the measures of the three angles are 42 degrees, 73 degrees, and 65 degrees.
Answered by
GPT 3.5
To find the value of x, we need to solve the equation:
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 that we have x, we can substitute it into each expression for the angles to find their measures:
First angle: 2x = 2(21) = 42 degrees
Second angle: 3x + 10 = 3(21) + 10 = 73 degrees
Third angle: 4x - 19 = 4(21) - 19 = 65 degrees
Therefore, x = 21 and the measures of the three angles are 42 degrees, 73 degrees, and 65 degrees.
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 that we have x, we can substitute it into each expression for the angles to find their measures:
First angle: 2x = 2(21) = 42 degrees
Second angle: 3x + 10 = 3(21) + 10 = 73 degrees
Third angle: 4x - 19 = 4(21) - 19 = 65 degrees
Therefore, x = 21 and the measures of the three angles are 42 degrees, 73 degrees, and 65 degrees.
Answered by
GPT 3.5
To find the value of x, I need to solve the equation:
2x + 3x + 10 + 4x - 19 = 180
Combining like terms:
9x - 9 = 180
Adding 9 to both sides:
9x = 189
Dividing both sides by 9:
x = 21
Now that I have x, I can substitute it into each expression for the angles to find their measures:
First angle: 2x = 2(21) = 42 degrees
Second angle: 3x + 10 = 3(21) + 10 = 73 degrees
Third angle: 4x - 19 = 4(21) - 19 = 65 degrees
So, x = 21 and the measures of the three angles are 42 degrees, 73 degrees, and 65 degrees.
2x + 3x + 10 + 4x - 19 = 180
Combining like terms:
9x - 9 = 180
Adding 9 to both sides:
9x = 189
Dividing both sides by 9:
x = 21
Now that I have x, I can substitute it into each expression for the angles to find their measures:
First angle: 2x = 2(21) = 42 degrees
Second angle: 3x + 10 = 3(21) + 10 = 73 degrees
Third angle: 4x - 19 = 4(21) - 19 = 65 degrees
So, x = 21 and the measures of the three angles are 42 degrees, 73 degrees, and 65 degrees.