Find all three angles

Question

Find measures of all three angles of the triangle in which the middle angle is 130 degrees smaller than eight times the smallest angle, and the largest angle is ten degrees larger than three times the smaller angle.

Answer 1

Hi Pookie, let x represent the smallest angle. Then 8x - 130 would represent the middle angle and 3x + 10 would represent the largest angle.

 

The sum of the angles in a triangle equals 180 degrees. If we add up the three angles, they will equal 180 degrees.

 

x + (8x - 130) + (3x + 10) = 180

 

x + 8x - 130 + 3x + 10 = 180

 

Combine terms:

 

12x - 120 = 180

 

Add 120 to both sides:

 

12x = 300

 

Divide both sides by 12:

 

x = 25

 

The smallest angle is 25 degrees.

 

The middle angle, 8x - 130, is 8 * 25 - 130 or 70 degrees.

 

The largest angle, 3x + 10, is 3 * 25 + 10 or 85 degrees.

 

Check:

 

25 + 70 + 85 = 180

 

180 = 180

 

Values check.

 

Questions?