Answer: 24°
Step-by-step explanation: Remember that when the ratio of the angles is 2 : 5 : 8, we can represent the angles as followed.
2x → first angle
5x → second angle
8x → third angle
Now, since the measures of the angles of a triangle add up to 180°, we can set up an equation to represent this.
2x + 5x + 8x = 180
We can simplify on the left side of the equation.
15x = 180
÷15 ÷15 ← divide both sides by 15
X = 12
Now to find the measure of the smallest angle, we simply plug 12 back in for x. Our first angle 2x measures 2 × 12 which is 24.
Therefore, the smallest angle is 24°.