Since the measure of the inner angles of a triangle is
(n - 2)180° = (3 - 2)180° = 1 * 180° = 180°, that means if the ratio is 3:5:10 that 180° is being divided into (3 + 5 + 10) or 18 sections.
Since there are 18 sections and 3 go to the smallest part, that means that it is [tex] \frac{3}{18} [/tex] of the total inner angle measure, or
[tex]180* \frac{3}{18}\\
10 * 3\\
30[/tex]
So the measure of the smallest angle is 30°.
