Question

find the measures of the angles of a triangle whose angles are in the ratio of 2:3:4. also, what kind of triangle is it?

Explanation:

Step1: Let the angles be 2x, 3x, 4x

Since the sum of angles in a triangle is 180°.

Step2: Set up the equation

$2x + 3x+4x=180$

Step3: Combine like - terms

$9x = 180$

Step4: Solve for x

$x=\frac{180}{9}=20$

Step5: Find the angles

$2x = 2\times20 = 40$; $3x=3\times20 = 60$; $4x = 4\times20=80$

Step6: Classify the triangle

Since all angles (40°, 60°, 80°) are less than 90°, it is an acute - angled triangle.

Answer:

The angles are 40°, 60°, 80°. It is an acute - angled triangle.