Dragan

CPhill is (this time)correct.

Line WO bisects angle MOX and it's parallel to XY

Line VO bisects angle NOZ and it's parallel to YZ

∠WOV = ∠XYZ = 180° - ( 40° + 17.5° )

∠ABC = 120°

∠YBC = 90°

∠BYC = ∠BCY = 45°

∠XBY = ∠YBX = 30°

∠AXY = 150°

∠XAY = ∠BAC = 15°

∠BAC = 15°      

In triangle ABC, we have AB=3 and AC=4. Side BC and the median from A to BC are of equal length, as in the picture below:

Hi booksly002, in order to find out angle A, you need to calculate side BC first.

Side  BC ≈ 3.163    

ABC, AB = BC = 25 and AC = 40. What is sin angle ACB?

cos(ACB) = 20/25 = 36.87°

sin(36.87°) = 0.6

AB => a = 3

BC => b = 4

CA => c = 5

Area of triangle is:                  A = ab/2 = 6 u²

Area of AB semicircle is:         A = [(a/2)² * pi] /2  = 3.534291735 u²

Area of BC semicircle is:         A = [(b/2)² * pi] /2  = 6.283185307 u²

Area of AC semicircle is:         A = [(c/2)² * pi] /2  = 9.817477043 u²

Tota area is:                             A_t = A + A + A = 15.81747704 u²

Area of a shaded region is:      A_s = A_t - A = 6 u² 

These areas are equal:          A = A_s    

The type of triangle must be specified! We can only assume that this is an isosceles triangle.  

perimeter of a rhombus is 68 one diagonal is 16 what is the lenth of the secound diagonal

Diagonal    D = {sqrt [(68/4)² - (16/2)²]} * 2 = 30  

I couldn't upload an image so I tried to get it linked!

https://free-picload.com/image/qJ0Mu3 

a = √25 = 5

b = √32 = 5.656854249

c = AB = ?

∠C = 81.86989765º

The law of cosines:          c² = a² + b² - 2ab * cos(C)

                                         c² = 25 + 32 - 56.56854249 * 0.141421356

                                         c² = 57 - 8

                                         c = 7  

1)    That angle is  105º        ( Tthis works with 30-60-90 triangles only )

I tried using  20-70-90 triangle, and the result was 108º, plus black (red) line doesn't bisect the top right angle.

What about the air inside the ball? Technically that air is within the cube too.  

The question should've stated that it was a solid ball.