This Week's Work : Week 15 - for Inquisitive Young Mathletes

Part I work for this week:

See if you can write proof to show the exterior angle of any regular convex polygon is \(\frac{360}{n}\).
I'll include that in my blog for better proof.

Polygons Part I : interior angle, exterior angle, sum of all the interior angles in a polygon, how many diagonals
in a polygon

Polygons Part II : reviews and applicable word problems

Interior angles of polygons from "Math Is Fun"

Exterior angles of polygons from "Math Is Fun"

Supplementary angles

Complementary angles

Get an account from Alcumus and choose focus topics on "Polygon Angles" to practice.
Instant feedback is provided. This is by far the best place to learn problem solving, so make the best use of
these wonderful features.

This week's video on math or science : Moebius Transformations Revealed

Part II work online timed test word problems and link to key in the answers will be sent out through e-mail.

Have fun problem solving !!

2013 Mathcounts State Prep : Angle Bisect and Trisect Questions

Proof : 
2y = 2x + b (exterior angle = the sum of the other two interior angles)
--- equation I

y = x + a (same reasoning as above)
--- equation II

Plug in the first equation and you have
2y = 2x + 2a = 2x + b

2a = b

  
Here is the link to the Angle Bisector Theorem, including the proof and one example.

Angle ABC and ACB are both trisected into three congruent angles of x and y respectively. 
If given angle "a" value, find angle c and angle b.  

Solution: 3x + 3y = 180 - a

From there, it's very easy to find the value of x + y
and get angle c, using 180 - (x + y).

Also, once you get 2x + 2y, you can use the same method -- 180 - (2x + 2y) to get angle b