Question

How to find angle OTS

Answer 1

Answer:

∠OTS = 180° - a - b/2  (where a and b are given but hard to read).

I think they're a = 25° and b = 127°, in which case,

∠OTS = 180° - 25° - 63.5° = 91.5°.

Of course, if I've misread the numbers, you'll have to fix that bit up.

Hope that helps!

Step-by-step explanation:

Let x = ∠OTS.

Triangle OTS is isosceles since OT = OS are radii.  So ∠OST = ∠OTS = x.

I'm not sure I can read the numbers correctly in the photo, so for the moment, put a = ∠OPS and b = ∠POT.  These are the given angles in the diagram, so we want x in terms of a and b.

As above, triangle OPS is also isosceles, so ∠OSP = ∠OPS = a.

The sum of the interior angles of the quadrilateral OPST is 360°, so

a + b + x + ( a + x ) = 360°

=> 2x = 360° - 2a - b

=> x = 180° - a - b/2.