Question

The measure of all of the interior angles of a triangle are in the extended ration 1 : 2 : 3. Which of the following choices is the value of the smallest angle?
A. 20 degrees

B. 30 degrees

C. 60 degrees

D. None of the choices are correct.

Answer 1

Let the angles be in the ratio of 1:2:3 which is given.
The smallest angle is x
The next angle is 2x
The largest angle is 3x

All triangles have 180 degrees.

x + 2x + 3x = 180
6x = 180 
x = 180/6
x = 30 degrees. The smallest angle is 30 degrees.

Answer 2

The total of ratio units is 1 +2 +3 = 6.
The total of angles in a triangle is 180°.
Each ratio unit stands for 180°/6 = 30°.
The smallest angle is 1 ratio unit, so is 30°, matching the 2nd selection.