To find the value of x in the triangle with angles 2x, 3x, and 4x degrees, we start by recalling that the sum of the angles in any triangle is always 180 degrees.
We can set up the equation as follows:
2x + 3x + 4x = 180
This simplifies to:
9x = 180
Now, we can solve for x by dividing both sides by 9:
x = 180 / 9
Thus, x = 20 degrees.
Now that we have the value of x, we can find the measures of each angle:
- First angle: 2x = 2 * 20 = 40 degrees
- Second angle: 3x = 3 * 20 = 60 degrees
- Third angle: 4x = 4 * 20 = 80 degrees
In summary, the angles of the triangle are 40 degrees, 60 degrees, and 80 degrees, confirming that they add up to 180 degrees, as expected for a triangle.