SOLUTION: The circle shown below is centered at O, has radius equal to 1, and theta=24. What is the sum of angles ACB and OAB?

 = 24 degrees is the central angle (it is shown not in the scale in your figure).


Triangle OAB is an isosceles triangle, and the angle OAB is the angle "at the base" AB;

So the measure of the angle OAB is   = 78 degrees.



Next, ACB is an inscribed angle, leaning on the same arc AB as the angle .


Therefore, the measure of the angle ACB is half of that for , i.e. 12 degrees.


The sum of measures of angles ACB and OAB is 78 + 12 = 90 degrees.    ANSWER