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O is the centre of this circle.
Calculate the size of angle x.
Show all of your working and state any theorems that you use.

O is the centre of this circle Calculate the size of angle x Show all of your working and state any theorems that you use class=


Answer :

Answer:  52 degrees

Explanation

Use the inscribed angle theorem to determine the following two arc measures:

  • arc JKM = 2*(angle MNJ) = 2*80 = 160 degrees
  • arc LMJ = 2*(angle LKJ) = 2*126 = 252 degrees

Then notice how,

(arc LMJ) + (arc JKL) = 360

(252) + (arc JKL) = 360

arc JKL = 360-252

arc JKL = 108

And finally one last bit of steps.

(arc JKL) + (arc LM) = arc JKM

(108) + (arc LM) = 160

arc LM = 160-108

arc LM = 52

Recall that arc measures are the same as the central angle measures. So knowing that arc LM is 52 degrees leads to central angle LOM being the same measure. Therefore, x = 52 is the final answer.

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