The interior angles of a triangle are in the ratio 2:3:4. What is the measure of the greatest exterior angle of the triangle?
Show answer & explanation
Correct answer: C
Explanation
Ratio of interior angles = 2 : 3 : 4
Sum of the angles of a triangle = 180°
Exterior angle = 180° − Interior angle
Let the angles be 2x, 3x, and 4x.
2x + 3x + 4x = 9x = 180
x = 20
The angles are 40°, 60°, and 80°.
The largest exterior angle = 180° − 40° = 140°