Question

Help!!! The measure of the central angle is ____________ the measure of the circumference angle.

Answer 1

Twice

The central angle theorem states that the central angle from two chosen poinfs A and B on the circle is always twice the inscribed angle from two points.

Please see the attached picture

Draw a line from the point O to point P

OP = OA = OB = radius

<APO = a , <BPO = b

<PAO = a , < PBO = b

( isosceles triangle)

<POA = 180 - 2a

<POB = 180 - 2b

All Angles at centre O must add up to 360°

< AOB = 360 - ( 180 - 2a ) - ( 180 - 2b )

<AOB = 2a + 2b

<AOB = 2 ( a + b )

Hope this helps...

Answer 2

Hi there! Hopefully this helps!

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Answer: Twice.

The measure of the central angle is two times the measure of the circumference angle.