Question
Prove that the angle in a segment greater than a semi-circle is less than a right angle.
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Answer
Given: $\angle\text{ACB}$ is an angle in minor segment.To prove: $\angle\text{ACB}<90^\circ$
Proof: By degree measure theorem
$\angle\text{AOB}=2\angle\text{ACB}$
And $\angle\text{AOB}<180^\circ$
Then, $2\angle\text{ACB}<180^\circ$
$\Rightarrow\angle\text{ACB}<\frac{180^\circ}{2}$
$\Rightarrow\angle\text{ACB}<90^\circ$
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