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 and the measures of all the three angles
To find the value and measures of all three angles, we can set up an equation using the fact that the sum of the angles in a triangle is always 180 degrees.
Let's denote the three angles as follows:
Angle 1: 2x
Angle 2: 3x + 10
Angle 3: 4x - 19
Now, we can set up the equation:
Angle 1 + Angle 2 + Angle 3 = 180
2x + (3x + 10) + (4x - 19) = 180
Combine like terms:
2x + 3x + 4x + 10 - 19 = 180
9x - 9 = 180
Add 9 to both sides:
9x - 9 + 9 = 180 + 9
9x = 189
Divide both sides by 9:
(9x)/9 = 189/9
x = 21
Now that we have found the value of x, we can substitute it back into the angles to find their measures.
Angle 1 = 2x = 2 * 21 = 42 degrees
Angle 2 = 3x + 10 = 3 * 21 + 10 = 73 degrees
Angle 3 = 4x - 19 = 4 * 21 - 19 = 85 degrees
So, the measures of the three angles are:
Angle 1 = 42 degrees
Angle 2 = 73 degrees
Angle 3 = 85 degrees.