Question

the ratio of interior angle measures of a triangle is 2:3:4. what are the angle measures? write the angle measures in order from least to greatest.
a. ( 20^circ, 30^circ, 40^circ )
b. ( 30^circ, 60^circ, 90^circ )
c. ( 40^circ, 60^circ, 80^circ )
d. ( 62^circ, 63^circ, 64^circ )

Explanation:

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

Since the sum of interior angles of a triangle is \(180^{\circ}\), we have the equation \(2x + 3x+4x=180^{\circ}\)

Step2: Solve for \(x\)

Combine like - terms: \(9x = 180^{\circ}\), then \(x=\frac{180^{\circ}}{9}=20^{\circ}\)

Step3: Calculate each angle

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:

C. \(40^{\circ},60^{\circ},80^{\circ}\)