Question

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

Answer 1

Given:

$\angle ACB$ is an angle in major segment.

Then,

We have to prove that $\angle ACB<{90}^0$

By degree measure theorem

$\angle ADB=2\angle ACB$

And $\angle ADB<{180}^0$

Then,

We get $2\angle ACB<{180}^0$

$\angle ACB<{90}^0$

The angle in a segment greater than a semi-circle is less than a right angle.