Question

Find the measures of the angles in a triangle with the ratio of 2:7:9

Answer 1

Answer: 20, 70, 90

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Work Shown:

Let x be some positive real number.

Multiply each part of the given ratio by x to get 2x:7x:9x

So we have the three angles 2x, 7x, and 9x.

For any triangle, the three angles must add to 180

2x+7x+9x = 180

18x = 180

x = 180/18

x = 10

This leads to

• 2x = 2*10 = 20
• 7x = 7*10 = 70
• 9x = 9*10 = 90

The three angles of this triangle are: 20, 70, 90

This is a right triangle due to the 90 degree angle.