Question
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. * 2 points
Answers
GPT 3.5
In a triangle, the sum of the measures of the three angles is always 180 degrees.
Therefore, we can write the following equation:
2x + 3x + 10 + 4x - 19 = 180
Combining like terms, we get:
9x - 9 = 180
Adding 9 to both sides of the equation, we have:
9x = 189
Dividing by 9 on both sides, we get:
x = 21
Now, we can substitute the value of x back into the equations to find the measures of the three angles:
Angle 1: 2x = 2(21) = 42 degrees
Angle 2: 3x + 10 = 3(21) + 10 = 63 + 10 = 73 degrees
Angle 3: 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.
Therefore, we can write the following equation:
2x + 3x + 10 + 4x - 19 = 180
Combining like terms, we get:
9x - 9 = 180
Adding 9 to both sides of the equation, we have:
9x = 189
Dividing by 9 on both sides, we get:
x = 21
Now, we can substitute the value of x back into the equations to find the measures of the three angles:
Angle 1: 2x = 2(21) = 42 degrees
Angle 2: 3x + 10 = 3(21) + 10 = 63 + 10 = 73 degrees
Angle 3: 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.