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The second largest and the smallest angles of a triangle are in the ratio of 3 : 1. The difference between the second largest angle and the smallest angle of the triangle is equal to 34°. What is the difference between the smallest and the largest angles of the triangle?

The second largest and the smallest angles of a triangle are in the ratio of 3 : 1. The difference between the second largest angle and the smallest angle of the triangle is equal to 34°. What is the difference between the smallest and the largest angles of the triangle? Correct Answer 95°

Let the second largest and the smallest angles of a triangle are 3x and x respectively.

3x – x = 34°

⇒ x = 34/2 = 17°

3x = 3 × 17 = 51°

We know that,

Sum of angles in a triangle = 180°

⇒ Largest angle = 180 – 17 – 51 = 112°

∴ The difference between the smallest and the largest angles of the triangle = 112 – 17 = 95°

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