Question

Need help can anyone help me???​

Answer 1

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.