Question 54

In $$\triangle $$ ABC,if the ratio of angles is in the proportion 3 : 5 : 4, then the difference between the biggest and the smallest angles (in degrees)is:

Solution

We know that sum of the all angles of the triangle is equal to the 180$$\degree$$.

Let the angles be 3x, 5x and 4x.

so, 3x + 5x + 4x = 180

x = 15

Smallest angle = 3x = 3 $$\times$$ 15 = 45$$\degree$$

Biggest angle = 5x = 5 $$\times$$ 15 = 75$$\degree$$

Difference between the biggest and the smallest angles = 75 - 45 = 30$$\degree$$

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