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Find the smallest angle, if one acute angle of the right-angled triangle is half of the other.

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90^{o}

60^{o}

40^{o}

30^{o}

answer is D.

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Detailed Solution

Given that, the acute angle is half of the other.
Let the acute angle be

x

. Then the other angle is

2 x

.
Drawing the figure from the given data.
Question Image

In triangle ABC, the sum of angles of a triangle is

180^{o}

. So,

⟹

90^{o} + 2 x + x = 180^{o}

⟹

3 x = 180^{o} - 90^{o}

⟹

x = \frac{90^{o}}{3}

⟹

x = 30^{o}

Hence, the angles are,

x = 30^{o}

2 x = 2 \times 30^{o}

= 60^{o}

.
Hence,

30^{o}

is the smallest angle.
Therefore, option 4 is correct.

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