If the angles of a triangle are in the ratio 2:3:4, what is the measure of the largest angle?

To find the measure of the largest angle in a triangle where the angles are in the ratio 2:3:4, start by letting the angles be represented by 2x, 3x, and 4x.

The sum of the angles in any triangle is always 180 degrees. Therefore, you can set up the equation:

2x + 3x + 4x = 180.

This simplifies to:

9x = 180.

To find the value of x, divide both sides of the equation by 9:

x = 20.

Now, substitute x back into each expression for the angles:

• The first angle is 2x, which is 2(20) = 40 degrees.
• The second angle is 3x, which is 3(20) = 60 degrees.
• The largest angle, represented by 4x, is 4(20) = 80 degrees.

Since the largest angle corresponds with the ratio of 4, the measure of the largest angle in the triangle is confirmed to be 80 degrees.