i duno how to do~
the first one is all substitution.Originally Posted by xiaoz
so substitute 8 for n
and solve
number 2 asks you to solve for n, so lets do it...
use the distributive property
simplify
multiply both sides by n
subtract 180n from both sides
subtract
divide both sides by A-180
simplify
simplify
and thats what n equals. Substitute the given number for A (157.5)
and solve, this will give you the answer for a.ii
Hello, xiaoz!
i duno how to do~
a) The measurement of an interior angle of a regular polygon of sides
. . . is given by the formula: . **
(1) Find the measure of an interior angle of a regular polygon with 8 sides.
How about plugging in ?
This requires some knowledge of Algebra I . . . too bad!(2) Write in terms of .Hence, find the number of sides
of the regular polygon with interior angles measuring 157.5° each.
We have: .
Multiply both sides by
Then: .
Factor: .
We are told that
Plug it in and determine
(3) Find the regular polygon such that when the number of sides is doubled
the measure of an interior angle is doubled.
This is the only one that's tricky . . .
For sides, the angle is: . [1]
For sides, the angle is: . [2]
Equate [1] and [2]: .
. . which simplifies to: .
. . which factors: .
. . and has the positive root: .
This checks out.
With we have an equilateral triangle: interior angle
Double the number sides and we have a hexagon: interior angle
. . . . . . . . ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
**
This is a really stupid way of writing the formula!
The proper form is: .
It can be shown that the sum of interior angles of any n-gon is:
If all angles are equal, each angle measures: . degrees.
Someone is going to say, "What's the difference? .They're equal!"
Well, that is certainly true.
This means that we will have dozens of formulas to memorize . . .
. . .
Catch my drift?