If the angles of triangle ABC are in the ratio 2:3:4, what is the measure of the largest angle?
Correct Answer: 80 degrees
- Step 1: Understand that the angles of triangle ABC are in the ratio 2:3:4.
- Step 2: Assign a variable 'x' to represent a common factor 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 degrees.
- Step 6: 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 is 80 degrees.
- Angle Ratios in Triangles – Understanding how to set up equations based on the ratio of angles in a triangle and applying the triangle sum theorem.
- Solving Linear Equations – Ability to solve for a variable in a linear equation derived from the sum of angles.
