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

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

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

Step 1: Understand that the angles of the triangle are in the ratio 2:3:4. This means we can represent the angles as 2x, 3x, and 4x, where x is a common multiplier.
Step 2: Write down the equation for the sum of the angles in a triangle. The sum of the angles in any triangle is always 180 degrees.
Step 3: Set up the equation: 2x + 3x + 4x = 180.
Step 4: Combine the terms on the left side of the equation: (2x + 3x + 4x) = 9x, so the equation becomes 9x = 180.
Step 5: Solve for x by dividing both sides of the equation by 9: x = 180 / 9.
Step 6: Calculate x: x = 20.
Step 7: Now, find the largest angle, which is represented by 4x. Multiply 4 by the value of x: 4x = 4 * 20.
Step 8: Calculate 4x: 4x = 80 degrees. This is the measure of the largest angle.

Triangle Angle Sum – The sum of the interior angles of a triangle is always 180 degrees.
Ratio and Proportion – Understanding how to express quantities in a given ratio and solve for unknowns.