Question

1. the ratio of the angles in a triangle is 2:3:4. what are the measures of the three angles?

Explanation:

Step1: Let the angles be \(2x\), \(3x\), \(4x\)

Since the sum of angles in a triangle is \(180^{\circ}\), we can use this property.

Step2: Set up the equation

\(2x + 3x+4x=180^{\circ}\)
\(9x = 180^{\circ}\)

Step3: Solve for \(x\)

\(x=\frac{180^{\circ}}{9}=20^{\circ}\)

Step4: Find the measures of the angles

First angle: \(2x = 2\times20^{\circ}=40^{\circ}\)
Second angle: \(3x = 3\times20^{\circ}=60^{\circ}\)
Third angle: \(4x = 4\times20^{\circ}=80^{\circ}\)

Answer:

The measures of the three angles are \(40^{\circ}\), \(60^{\circ}\), and \(80^{\circ}\)