One angle of a triangle is $60^{\circ}$ and the other two angles are in the ratio 2:3. Find the smallest angle in the triangle.

$48^{\circ}$

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$59^{\circ}$

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$61^{\circ}$

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$63^{\circ}$

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Solution

The correct option is A
$48^{\circ}$

Let the other angles be 2x and 3x

Then, according to the angle sum property, $60^{\circ} + 2 x + 3 x = 180^{\circ}$

$5 x = 120^{\circ}$

$x = 24^{o}$

Hence, the smallest angle is $2 \times 24 = 48^{\circ}$ .

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One angle of a triangle is 60∘ and the other two angles are in the ratio 2:3. Find the smallest angle in the triangle.

The correct option is A 48∘ Let the other angles be 2x and 3x Then, according to the angle sum property, 60∘+2x+3x=180∘ 5x=120∘ x=24o Hence, the smallest angle is 2×24=48∘.

One angle of a triangle is $60^{\circ}$ and the other two angles are in the ratio 2:3. Find the smallest angle in the triangle.

The correct option is A
$48^{\circ}$

Let the other angles be 2x and 3x

Then, according to the angle sum property, $60^{\circ} + 2 x + 3 x = 180^{\circ}$

$5 x = 120^{\circ}$

$x = 24^{o}$

Hence, the smallest angle is $2 \times 24 = 48^{\circ}$ .