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Question 194
The ratio of angles of a triangle is 3 : 5 : 7. What is the difterence between double the smallest angle and half of the largest angle ?
Solution
We know that the sum of interior angles of a triangle is equal to $$180^{o}$$.
The total sum of the ratios must be equal to $$180^{o}$$.
Hence each angle of the triangle is $$\frac{3\times180}{15}=36^{o}$$ , $$\frac{5\times180}{15}=60^{o}$$ and $$\frac{7\times180}{15}=84^{o}$$
Twice the smallest angle $$=2\times36 = 72.$$
Half the largest angle $$=\frac{84}{2} = 42.$$
Difference $$=72-42 = 30.$$
Hence Option D is the correct answer.
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