he 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.
The sum of the angles in a triangle is 180 degrees. Therefore, we have the equation:
2x + (3x + 10) + (4x - 19) = 180
Combining like terms, we get:
9x - 9 = 180
Adding 9 to both sides, we have:
9x = 189
Dividing both sides by 9, we find:
x = 21
Now we can substitute this value back into the expressions for the angles 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
So the value of x is 21, and the measures of the three angles are 42 degrees, 73 degrees, and 65 degrees.