Question

The ratio of the measures of the angles of a triangle is 2:3:10. What is the smallest angle measure?

Answer 1

Given -

• The ratio of the measures of the angles of a triangle is 2:3:10.

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To find -

• Smallest angle of the triangle.

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Solution -

• Let the ratio of angles be x.

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All angles are

• First angle = 2x
• Second angle = 3x
• Third angle = 10x

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Since, sum of all angles of a triangle is 180.

Therefore,

→ 2x + 3x + 10x = 180

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→ 15x = 180

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→ x = 180/15

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→ x = 12

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Now, by putting the value of x we can calculate all the angles of the triangle.

• First angle = 2x = 24°
• Second angle = 3x = 36°
• Third angle = 10x = 120°

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Hence,

• The smallest angle of the triangle is 24°.

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Answer 2

Given :

• The ratio of the measures of the angles of a triangle is 2:3:10.

To Find :

• Smallest angle

Solution :

We know that sum of angles of a triangle = 180°

So Let's take 2:3:10 as 2x, 3x, 10x

⇒2x + 3x + 10x = 180°

⇒ 15x = 180°

⇒ x = 180/5

⇒ x = 12

Hence, the value of x = 12

So,

2x = 2 × 12 = 24

3x = 3 × 12 = 36

10x = 10 × 12 = 120

•°• The smallest angle is 24.