Question

Points A, B and Clie on the circumference of a circle, centre O.

LABC= 37°.
37
B
Diagram not drawn to scale
Q7
Q8 09 Q10 Q11 Q12
O
Calculate the size of the reflex angle ZAOB.
(2 marks)

Answer 1

286°

Explanation:

You want the measure of the reflex angle AOB, whose vertex is the center of the circle in which inscribed angle ACB has measure 37°.

Inscribed angle

An inscribed angle is half the measure of the arc it intercepts, so short arc AB is 2·37° = 74°.

Central angle

A central angle is equal to the measure of the arc it intercepts. Long arc ACB is 360° -74° = 286°. That means the measure of the reflex central angle AOB is ...

reflex ∠AOB = 286°

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Additional comment

The total of arcs around a circle is 360°.