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Q.

The acute angles of a right triangle have a ratio of $\frac{2}{3}$ . What is the difference between the two angle measures?

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a

42

°

b

54

°

c

18

°

d

72

°

answer is C.

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Detailed Solution

Given, the ratio of acute angles of a right-angled triangle is

\frac{2}{3}

.
We know that the sum of the angles in any triangle

= 180^{o}

.
Let the measure of the acute angles be

2 x

and

3 x

.

2 x + 3 x + 90^{o} = 180^{o}

\Rightarrow 5 x + 90^{o} = 180^{o}

\Rightarrow 5 x = 90^{o}

\Rightarrow x = 18^{o}

\Rightarrow 2 x = 36^{o}

\Rightarrow 3 x = 54^{o}

The measures of the acute angles in a right triangle are

36^{o}

and

54^{o}

.
Therefore, the difference between the two angles

= 54^{o} - 36^{o} = 18^{o}

.
Hence, the correct option is 3.

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