The ratio of the angle measures 1: 2: 2. what is the value of the smallest angle?

So, there are 3 sides, meaning is a triangle with 3 angles.

now, we know the interior angles of a triangle add up to 180°.

these 3 angles are at a ratio of 1:2:2 with each other... so what we do is simply split 180 into (1+2+2) equal pieces, and give 1 piece to one, 2 to the other and 2 to the last one.

180/(1+2+2)  is 36

so the angle with ratio of 1 takes 1(36)

the angle with ratio of 2 takes 2(36)

and the last angle also takes 2(36).

you can add them up if you wish, they are 180°.