The measures of three angles of a triangle given by 3x + 1, 2x - 3, and 9x. What is the measure of the smallest angle?

Answer 1

Greetings! Lets solve this shall we?

Note: The sum of the measures in a triangle equal to 180 degrees! Also, note that

Angle 1 : 3x + 1

Angle 2: 2x - 3

Angle 3: 9x

Then, (3x+1) + (2x-3) + 9x = 180 so we can evaluate the equation.

(3x+1) + (2x-3) + 9x = 180

14x - 2 = 180

14x =182

x = 13

Now we must find out which angle is the smallest?

Angle 1 : 3x + 1 = 3(13) + 1 = 40°

Angle 2: 2x - 3 = 2(13) - 3 = 23°

Angle 3: 9x = 9(13) = 117°

23 degrees is the smallest angle!

I hope this helped!