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

1.	Prove that the angle in a segment greater than a semi-circle is less than a right angle.
Answer» Given that, ∠ACB is an angle in major segment To prove : ∠ACB > 90° Proof : By degree measure theorem, ∠AOB = 2∠ACB And, ∠AOB < 180° Then, 2∠ACB < 180° ∠ACB < 90° Hence, proved

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

Answer»

Given that,

∠ACB is an angle in major segment

To prove : ∠ACB > 90°

Proof :

By degree measure theorem,

∠AOB = 2∠ACB

And,

∠AOB < 180°

Then,

2∠ACB < 180°

∠ACB < 90°

Hence, proved

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

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