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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 ?
- A25
- B36
- C38
- D30
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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.
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.