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
To find the value of x, we can set up an equation:
2x + 3x + 10 + 4x - 19 = 180
Combining the like terms, we get:
9x - 9 = 180
Adding 9 to both sides of the equation:
9x = 189
Dividing both sides by 9:
x = 21
Now we can substitute the value of x back into the expressions for the angles:
2x = 2(21) = 42 degrees
3x + 10 = 3(21) + 10 = 73 degrees
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.