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If the angles of the triangle are in the ratio 2 : 3 : 4, find all the three angles.
Question

If the angles of the triangle are in the ratio 2 : 3 : 4, find all the three angles.

A.

40°, 60°, 80°

B.

20°, 40°, 60°

C.

30°, 60°, 90°

D.

90°, 180°, 360°

Correct option is A

Given:

The angles of the triangle are in the ratio 2 : 3 : 4.

Formula Used:

1. The sum of the angles of a triangle:
Sum of angles = 180^\circ

2. Let the angles be 2x, 3x, and 4x . Use the equation:
2x + 3x + 4x = 180^\circ

Solution:

1. Solve for x :
2x + 3x + 4x = 180^\circ
9x = 180^\circ
x = 20^\circ

2. Find the three angles:
- First angle: 2x = 2 \times 20 = 40^\circ
- Second angle: 3x = 3 \times 20 = 60^\circ
- Third angle: 4x = 4 \times 20 = 80^\circ

Final Answer:

The three angles of the triangle are **40°, 60°, and 80°**.

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