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Answer

Let the center of the circle be O.

So, Angle AOC is 180 – 68- 45 = 67°

Therefore Angle q is 180 – 67 – 38 = 75°

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We know that opposite angles are equal (the red ones).
So q + 38 = 68 + 45, which means
   q = 68 + 45 - 38 = 68 - 38 + 4 = 30 + 45 = 75.
  (I wrote this out to show that a calculator isn't necessary.
   You can do this mentally too. Not even a "carry-over"!)

For the sake of speed in exam, it is better to apply known
geometry facts (opposite angles are equal) than to work out
all the intermediate angles.

Less working means less chance of error too.

 

0 Replies 2 Likes