Arc

I'll try a few

In the first one.....these chords have the same length....so....this implies that

(7x - 39)°  = 87°

7x - 39   = 87      add 39 to both sides

7x  =  126        divide both sides by 7

x  = 18

Second one.....same thing.....the chords LM and NP have the same length

So

41 - 2x  = 7x  +  5         add  2x to both sides.....subtract 5 from both sides

36  = 9x      divide both sides by  9

4   = x

So 

LM  = 41 - 2x   =   41 - 2(4)   =  41  - 8   =   33

Third one

Since chords  DE  = GF....equal chords are the came distance from the center of the circle

This implies that  HJ  = JI   ....so....

3x + 20  =  15x  - 64         add 64 to both sides, subtract 3x from both sides

12x  = 84    divide both sides by 12

x  = 7

So JI   = 15x - 64  =  15(7) - 64  =  105 - 64  = 41

Fourth one

LM and NP  are equal distances from the center of the circle....so....they have equal length

Then.....they also span the same arcs

This implies that

(8x - 56)°  = (5x + 22)°

8x - 56  =  5x + 22          add 56  to both sides, subtract 5x from both sides

3x =  78      divide both sides by 3

x  =  26

So  LM spans an arc of   8(26) - 56  = 208 - 56  = 152°

And NP spans the same arc

So  LP  spans an arc  = 360 - LM - NP - MN =

(360 - 152  -152  - 39)°   =    17°

Last one

Equal segments drawn from the center of the circle meet chords BC and CD at right angles

This means that the two chords are equal and thus, they span the same arcs....so....like before...

9x - 53  = 2x + 45     add 53 to both sides  and subtract 2x form both sides

7x = 98     divide both sides by 7

x  = 14

So  each chord spans an arc of  9(14)  - 53  = 73°

Then BAD  will span  an arc  =  360 - 73 - 73   = 214°