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The angles of a triangle are in the ratio of $3 : 5 : 7 .$ What is the measure of the largest interior angle of the triangle?

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18^{o}

48^{o}

84^{o}

96^{o}

answer is C.

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Detailed Solution

Given that the angles of a triangle are in the ratio of

3 : 5 : 7 .

By angle sum property, the sum of angles is

180^{o}

.
Let

3 x, 5 x

and

7 x

be the three angles of the triangle.
So,

\Rightarrow 3 x + 5 x + 7 x = 180^{o}

\Rightarrow 15 x = 180^{o}

\Rightarrow x = 12^{o}

Since 7x > 5x > 3x, we know that 7x is the largest angle.
Hence, Largest interior angle,

\Rightarrow 7 \times 12^{o} = 84^{o}

Thus, the largest angle is

84^{o}

.
Therefore, the correct option is 3.

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