Answer:
it is greater than 45°
Step-by-step explanation:
From the relationship of angles and secants/tangents, we have ...
m∠GSO = (long arc GO -arc GT)/2
Solving for (long arc GO), we have ...
2(m∠GSO) +arc GT = (long arc GO)
We know that (long arc GO) > 180°, so we can write ...
2(m∠GSO) +90° > 180° . . . . arc GT = 90°
2(m∠GSO) > 90° . . . . . . subtract 90°
m∠GSO > 45° . . . . . . . . divide by 2
_____
Alternate solution
Inscribed ∠GOT has half the measure of arc GT, so is 45°.
You know that if angle G were 90°, then the right triangle would be isosceles, and angle S would also be 45°. In this triangle, arc GTO is less than 180°, so angle G is less than 90°.
When angle G gets smaller, the sum of angles remains the same, so angle S must be larger than 45°.
This reasoning is written more formally in the math above.
