Is there a 10 sided polyg with 9 interior angles of 150 degrees each? what the measure of 10th int. angle?

Question

Can you explain the formula for the diagrams and be specific regarding the 2 three dimensional shapes and say why so that I may understand regarding the previous questions? Also can you state the proof without words of the Pythagorean Theorem for diagrams of a diamond, and a square?

Answer 1

n = 10
Sum of all angles = 180 (n - 2)
= 180(10 - 2)
= 180 * 8
= 1440 degrees

Sum of 9 angles = 9 * 150
= 1350

Measure of 10th angle = 1440 - 1350
= 90 degrees



The formula I used to answer your previous question was:

Volume of cuboid = l*b*h
where l = 2, b = 4 and h = 8 units

Volume of cube = (side)^3
'^' is the exponent symbol

Surface Area (SA) of cuboid = 2(lb + bh + hl)
SA of cube = 6 * (side)^2


I'm sorry I cannot give diagrams here. Any proof of Pythagoras theorem is useless without a diagram. If you're looking for proofs with diagrams try these websites:

http://en.wikipedia.org/wiki/Pythagorean_theorem
http://www.cut-the-knot.org/pythagoras/index.shtml

If this was not sufficient or if you did not understand a proof, email me. Yahoo! Answers email service does not allow email attachments or pictures. If you are in real need of diagrams with a detailed explanation of the simpler proofs, I shall give them to you. You shall have to give me your email address though. I shall give you mine if you need it.

Answer 2

to get total interior angle: {No of sides-2}x180
(10-2)x180
8x180
1440

total interior angle of a decagon (10 sides) is 1440.
so 9x150= 1350 the bal: 90.