Question

Find the angle of a triangle if the first angle is 31 degrees more than the second and the third is 5 degrees less than twice the first

Answer 1

1. 54°
2. 23°
3. 103°

Explanation:

You want the angles of a triangle with the second angle 31 degrees less than the first, and the third angle 5 degrees less than twice the first.

First angle

In terms of the first angle (x), the sum of angles of the triangle is ...

x +(x -31) +(2x -5) = 180 . . . . . . . measures in degrees

4x -36 = 180 . . . . . . . . . . . . . simplify

x -9 = 45 . . . . . . . . . . . . . divide by 4

x = 54 . . . . . . . . . . . . . add 9

Other angles

Then the other angles are ...

(x -31) = 54 -31 = 23

(2x -5) = 2(54) -5 = 103

The angles of the triangle are 54°, 23°, and 103°.

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Additional comment

Our version of the problem statement expresses all of the angles in terms of the first angle. That simplifies writing the equation for their sum. "First is 31 degrees more than the second" is the same relationship as "Second is 31 degrees less than the first."

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