In degrees, what is the measure of the smallest angle in a triangle with angles in a ratio of 1:2:3?

To determine the smallest angle in a triangle with angles in the ratio of 1:2:3, we begin by understanding that the sum of all angles in any triangle is always 180 degrees.

Let's denote the angles based on the given ratio. We can express them as:

• The first angle is ( x ),

• The second angle is ( 2x ),

• The third angle is ( 3x ).

Now, if we set up the equation based on the sum of the angles:

[ x + 2x + 3x = 180 ]

This simplifies to:

[ 6x = 180 ]

To find ( x ), divide both sides by 6:

[ x = \frac{180}{6} = 30 ]

Now we can find each angle:

• The first angle is ( x = 30 ) degrees,

• The second angle is ( 2x = 60 ) degrees,

• The third angle is ( 3x = 90 ) degrees.

In this triangle, the smallest angle, represented by ( x ), measures 30 degrees. Therefore, the correct answer is 30 degrees, making it the smallest angle in the triangle