Prove that the angle in a segment greater than a semi-circle is less than a right angle.

Question

Philoid · Accepted Answer

Given that,

∠ACB is an angle in major segment

To prove: ∠ACB > 90^o

Proof: By degree measure theorem,

∠AOB = 2 ∠ACB

And,

∠AOB < 180^o

Then,

2 ∠ACB < 180^o

∠ACB < 90^o

Hence, proved