Question

[15 POINTS] Does anyone know how to solve this?

Can you also explain how to solve it and not just give answers?

Answer 1

The sum of the arcs of a circle is 360°.
.. (9x -22) +61 +(5x -7) +34 = 360
.. 14x +66 = 360 . . . . . . . . . . . . . . . . collect terms
.. 14x = 294 . . . . . . . . . . . . . . . . . . . . subtract 66
.. x = 21 . . . . . . . . . . . . . . . . . . . . . . . divide by 14

Then the unknown arcs are
.. (9*21 -22)° = 167°
and
.. (5*21 -7)° = 98°
_____
In summary
.. x = 21
.. GK = 167°
.. HJ = 98°
.. HGJ = 360° -98° = 262°
.. GKJ = 167° +34° = 201°