If the angles of triangle DEF are in the ratio 2:3:4, what is the measure of the

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

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

Step 1: Understand that the angles of triangle DEF are in the ratio 2:3:4.
Step 2: Assign a variable 'x' to represent a common multiplier for the angles. So, the angles can be expressed as 2x, 3x, and 4x.
Step 3: Write an equation for the sum of the angles in a triangle. The sum of the angles is 180 degrees, so we have: 2x + 3x + 4x = 180.
Step 4: Combine the terms on the left side of the equation. This gives us: 9x = 180.
Step 5: Solve for 'x' by dividing both sides of the equation by 9. This gives us: x = 20.
Step 6: Now, find the largest angle by substituting 'x' back into the expression for the largest angle, which is 4x. So, 4x = 4 * 20 = 80 degrees.
Step 7: Conclude that the measure of the largest angle in triangle DEF is 80 degrees.

Angle Sum Property of Triangles – The sum of the interior angles of a triangle is always 180 degrees.
Ratios – Understanding how to work with ratios to express relationships between quantities.