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Question
If the angles of a triangle are in the ratio 2 : 3 : 4 then the difference between the greatest and the smallest angle is _______
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Solution
40°
Explanation;
Hint:
Given angles are in the ratio 2 : 3 : 4
Let the angles be 2x, 3x and 4x
Since sum of the angles of a triangle is 180°,
We get 2x + 3x + 4x = 180
∴ 9x = 180
∴ x = `180/9` = 20°
∴ The angles are 2x = 2 × 20 = 40°
3x = 3 × 20 = 60°
4x = 4 × 20 = 80°
∴ Difference between greatest and smallest angle is 80° – 40° = 40°
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