The Interior Angle Equation of a Polygon

Here is an example of how the equation used to find the interior angle measure sum in polygons works.

Angle sum = (n-2)(180)

This is a Lamborghini that I photographed at a car show. Notice how the headlights form pentagons. Now we will test to see if the equation works.

To find the sum of the interior angles in a pentagon, the equation is (5-2)(180).

(5 - 2)(180)
= 3(180)
= 540

So, the total measure of all the angles in a pentagon equals 540 degrees. This equation should work for all pentagons, so now let's test to see if it works on the headlight.

As we can see, the measures of all the angles are: 54.56, 129.09, 103.2, 136.76, and 116.39. If we add these all together, we get 540, which proves the equation to be correct, for both regular and non-regular polygons. (~DM5)

Congruent Angles in a Stool

I noticed that a stool in my house had rungs that were parallel to each other. I figured that if the rungs were parallel then the corresponding angles would be congruent. After taking the picture and putting it into GSP, I found that angle BAF was indeed congruent to angle DCF. (~DM2)

Perfectly Perpendicular?

My family is currently renovating the kitchen, and the workers just put in the tile backsplash. Supposedly they have tools to make sure they place the tile perfectly, but I decided to see if it actually aligned. Surely if the tile was placed perfectly, then there should be a perpendicular line in between the tiles.

By definition, a perpendicular line is one that has a right angle (which is 90 degrees) on both sides. However, when I measured the angles of the tiles, it looks like the tile guys were a little off. One side is about 90.29 degrees and the other side is 89.71 degrees. It's pretty close but not perfect. Sorry guys but I just proved you wrong....It still looks really good though! (~JC2)

Isoceles Triangles

I was at swim practice the other day and I noticed that the backstroke flags were upside down isosceles triangles. Two of the sides of the flags are congruent and the angles opposite to those sides are congruent as well making it an isosceles triangle by the Isosceles Triangle Theorem. (~AD1)

Geometric Tiles

These tiles are an example of if two parallel lines are cut by a transversal, alternate interior angles are congruent. (~JZ5)

Tessellations in a Table

I saw a table and noticed it had tessellations in it. First off, the shapes are hexagons. This can be proved using the formula (n-2)180 where n is the number of sides and the sum should be the sum of the angles. So (6-2)180= 720 degrees.

The hexagons fit together at the intersections because the two smaller angles are about 50 degrees and the two larger angles are about 130 degrees.  Altogether it is 360 degrees.  This means there are no gaps in the tessellation, and it fits together well.  (~NW5)

PS4 Angles

I saw on my PS4 that front was made up of parallel lines, congruent angles and congruent shapes. To the left there are two congruent rectangles with lines on the top and bottom that are parallel to each other and same goes for the left side except the rectangles are bigger. (~DF5)