One angle of a triangle is 2 more than four times as large as the other angle. The third angle is three times the first angle decreased by 6. What is the measure of each angle?

the angles are

x, 4x+2, 3x-6

they add up to 180, so ...

To solve this problem, let's suppose the measure of the first angle is x degrees.

According to the given information, the second angle is 2 more than four times the first angle. So, the measure of the second angle is (4x + 2) degrees.

The third angle is three times the first angle decreased by 6. Therefore, the measure of the third angle is (3x - 6) degrees.

Since we know that the sum of the angles in a triangle is always 180 degrees, we can set up an equation to solve for x:

x + (4x + 2) + (3x - 6) = 180

Combining like terms, we have:

8x - 4 = 180

Adding 4 to both sides of the equation:

8x = 184

Dividing both sides by 8:

x = 23

So, the measure of the first angle is 23 degrees.

Now we can find the measure of the other two angles by substituting the value of x:

Second angle: 4x + 2 = 4(23) + 2 = 92 + 2 = 94 degrees

Third angle: 3x - 6 = 3(23) - 6 = 69 - 6 = 63 degrees

Therefore, the measure of each angle in the triangle is:
First angle: 23 degrees
Second angle: 94 degrees
Third angle: 63 degrees