Question

Simple question

In the circle above

P is the center
.
What is the value, in degrees, of 0?

____degrees

Answer 1

`\theta=45^\circ`

Explanation:

P is the centre of the circle and:

`\angle P=90^\circ`

Angle
`\theta` is the angle subtended by the same arc as P at the circumference.

By the Inscribed Angle Theorem, we know that angle subtended by an arc at the centre is twice the angle subtended by the same arc at the circumference.

Therefore:

`\angle P =2\theta\\2\theta=90^\circ\\\theta=90^\circ / 2\\\theta=45^\circ`