OUR FEARLESS LEADER!!!

Angles on the Same Arc

Angles on the same arc at the circumferance are equal, if one angle is pulled off the arc the two become supplemantary (they add to 180°)

The Angle in a Semicircle

This is super simple, the angle in a semicirle is always a right angle (90°).

Angle at the Centre of a Circle

My first circle investigation on Geometer's Sketchpad!!!
The angle at the centre of a circle is ALWAYS double the angle at the circumference.

Exterior Angles of a Polygon

This table shows all the interior and exterior characteristics of polygons:

Shape	Angle sum		Shape	Angle sum
Quadrilateral	360 º		Quadrilateral	360 º
Pentagon	540 º		Pentagon	360 º
Hexagon	720 º		Hexagon	360 º
Heptagon	900 º		Heptagon	360 º
Octagon	1080 º		Octagon	360 º
Nonagon	1260 º		Nonagon	360 º
Decagon	1440 º		Decagon	360 º

INTERIOR / EXTERIOR ANGLE SUM OF A QUADRILATERAL

Number five!!!

For this investigation I made a quadrilateral using rays and then measured the interior angles, I predicted that the sum of the angles would be 360°, and I was right!

The some of the exterior angles was also 360°.

Angles and Parallel Lines

This investigation shows that when two parallel lines are cut by another line (a transversal), corresponding and alternate angles are equal, and co-interior angles are supplementary (add to 180°)
Corresponding angles are on the same side of the transversal and face the same direction:





















Alternate angles are on opposite sides of the transversal and face opposite directions:


















Co-interior angles are on the same side of the transversal but face opposite directions:

Angle Sum Of A Triangle

This is simple but frighteningly useful, the three angles of a triangle ALWAYS add up to 180°

(Click to Enlarge)

Adjacent Angles

I SEE ANGELS!!!

No, wait, there angles.

(click to enlarge)

Opposite angles are equal, and when two angles that share the same vertices are added they equal 180°.

Notes taken from exercise:

-If two angles sum to 180º they are called supplementary angles.
-When two lines intersect, the vertically opposite angles are equal.
-The angle sum of a straight line is 180º.