1. The sum of the interior angles in a regular polgyon is equal to 180(n-2), where n is the number of sides of the polygon.

The regular polygons displayed on the right are cyclic polygons.

Note: Notice each pair of exterior angles are equal. Thus for each interior angle, there is one exterior angle. Any regular polygon has n interior angles and n exterior angles.

Select interior angles. Move the slider from 1 to 10 and study the pattern. The chart on the left side of the interactive activity is a record of the results. Look at the explation of exterior angles under the chart. Switch to to exterior angles on the interactive activity. Move the slider from 3 to 10 - the chart on the right is a record of the results.

2. The opposite angles of a cyclic quadrilateral are supplementary (total 180^o). Therefore the angles in a cyclic quadrilateral total 360^o.

Cyclic quadrilateral example:

<A + <B = 180^o
<C + <D = 180^o
<A + <B + <C + <D = 360^o.

or

Interactive Activity

• Adjust A, B, C and D to form a cyclic quadrilateral ADBC.
• Notice <A + <B = 180^o and <C + <D= 180^o.
• Hold the SHIFT key when you drag on the circumference of the circle to change the size of the circle.

Inscribed angles subtended by corresponding arcs are supplementary (total 180^o).

<A + <B = 180^o (arc DC/major arc DC)
<C + <D = 180^o (arc AB/major arc AB)
<A + <B + <C + <D = 360^o.

Interactive Activity

• Adjust A, B, C and D to form two pairs of inscribed angles subtended by corresponding arcs.
• Notice <A + <B = 180^o and <C + <D = 180^o.
• Hold the SHIFT key when you drag on the circumference of the circle to change the size of the circle.