1. What is size of angle A? 2. What is the size of angle B? I'm not sure what to do.?

 angle a = 60° - 25° = 45° (not 51°)
 The snowflake is completely symmetrical. Hence
 The 'dart' (which is a quadrilateral) angles 
 add to 25° + 315° + 2b or 360°.
 Hence angle b = 10°

Refer to the labeled figure below.

Since the 6 point snowflake is completely symmetrical, the purple circle contains 6 angles of 25° and 6 angles of a°.
6×25° + 6a° = 360°
25° + a° = 60°
a° = 35°

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As shown in the figure below, a dotted line is drawn to bisect one of the 6 quadrilaterals.

The snowflake is completely symmetrical.  Hence
c₁ + c₂ = 51°
e₁ + e₂ = 25°

c₁ is an exterior angle of a triangle, and c₂ is also an exterior of another triangle.
c₁ = e₁ + b° …… [1]
c₂ = e₂ + b° …… [2]

[1] + [2]:
c₁ + c₂ = (e₁ + e₂) + 2b°
51° = 25° + 2b°
2b° = 26°
b° = 13°

1. The full 360º can be broken down in six 25ºs and six α’s
6*25º + 6α = 360º
25º + α = 60º
α = 35º (not 51º)
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2. Each ‘dart’ is a quadrilateral so its internal angles add up to 360º.
25º + 2b + (360º - 51º) = 360º
25º + 2b  = 51º
2b = 26º
b = 13º

Just do it one step at a time, using each bit of information. You may have to guess as to the order of when you use one bit of information before another bit.
I will simply use the word "thing" for each of the six objects that are four-sided and closed.

For example, one bit of information is:
"It is completely symmetrical"

The complete turn around the centre (360 degrees) is divided into six equal parts of 60 degrees each.

Therefore, the right arm of the top "thing" is 60 degrees away from the right arm of the "thing" to its left. (Do mark it on a drawing, it helps)
The distance (angle) between these two lines is 60 (as we just found from the bit of information). The centre angle inside the thing is given as 25, therefore this leaves 60-25 = 35 for the outside angle (a)
By symmetry, all angles "a" are the same = 35
The sum of all centre angles is, therefore,
6*(25+35) = 360 = complete circle (which is what we want)

The thing's external outer angle (V shaped) is given as 51 degrees. This means that the inside angle of the point of the V must be 360-51 = 309

The thing itself is a closed polygon with 4 angles. The sum of inner angles for a four-angled figure is 360 (for example, a square has four 90-degree angles = 360).
Because of symmetry, the remaining tiny angles (both marked "b") must be equal to each other, and must share the remaining value, once we take away the other two angles.

Inside the thing:
one angle is 25 degrees
one angle is 309 degrees
This leaves 360 - 334 = 26
each "b" gets half of that