Enter your answer below. 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. (Please list just the numerical values with a space in between. No comamas. No variable
To find the value of x, we can set up an equation based on the fact that the sum of the angles in a triangle is always 180 degrees.
2x + 3x + 10 + 4x - 19 = 180
9x - 9 = 180
9x = 189
x = 21
Now we can substitute the value of x back into the expressions for each angle.
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 measures of the angles are 42 degrees, 73 degrees, and 65 degrees.