what is the measure of the angles

Question

 A triangle has one angle that measures 5 degrees more than twice the smallest angle, and the largest angle measures 11 degrees less than 3 times the measure of the smallest angle. Find the measures of the three angles. 

Answer 1

smallest = x

5 degrees more than twice the smaller angle = 2x + 5

11 degrees less than 3 times the smallest = 3x - 11

Then, all 3 angles add to 180.

x + (2x + 5) + (3x - 11) = 180

Combine like terms

6x - 6 = 180

6x = 186

Divide both sides by 6:

x = 31

Plug back in to the expressions above (replace x with 31):

Smallest: x = 31 degrees

Next biggest: 2(31) + 5 = 67 degrees

Largest angle: 3(31) - 11 = 82 degrees

Just to check: 31 + 67 + 82 = 180. All set!

Answer 2

Hi Vale

The angles are 31, 67, and 82 degrees

The three angles in Triangle sum to 180

Let x + y + z represent the angles in the triangle

Let x = smallest

Let y = 2x + 5

Let z = 3x - 11

x + 2x + 5 + 3x - 11 = 180

Combine like terms

6x - 6 = 180

Add 6 to both sides of the equation

6x = 186

Divide both sides by y

x = 31

y = 2x + 5 = 2(31) + 5 = 62 + 5 = 67

z = 3x - 11 = 3(31) - 11 = 93 - 11 = 82

x + y + z = 31 + 67 + 82 = 180