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Geometry, NAP-D4-NC29 SA

A star is drawn on the inside of a regular pentagon, as shown below.
 

What is the size of the angle marked `x`?

  degrees
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`36^@`

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`text(Consider the triangle)\ \ ABC\ \ text(in)`

STRATEGY: The internal angle sum is  3 × 180 = 540 (since 3 triangles can be drawn internally from one point).

`text(the pentagon,)`

`text(Total degrees in a pentagon)`

`= 3 xx 180`

`= 540^@`
 

`:.\ text(Internal angle)` `= 540/5`
  `= 108^@`

 
`DeltaABC\ text(is isosceles)`

`:. x + x + 108` `= 180`
`2x` `= 72`
`x` `= 36^@`

Geometry, NAP-F4-CA11

A six sided figure is drawn below.
  

What is the sum of the six interior angles? 

`540^@` `660^@` `720^@` `810^@`
 
 
 
  
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`720^@`

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`\text{Method 1}`

`text(Reflex angle) = 360-90 = 270^@`

`:.\ text(Sum of interior angles)`

`= (270 xx 2) + (30 xx 2) + (60 xx 2)`

`= 720^@`
 

`\text{Method 2}`

`text{Sum of interior angles (formula)}`

`= (n-2) xx 180`

`=4 xx 180`

`= 720^@`

Geometry, NAP-I4-CA25 SA

The sum of the interior angles of a 6 sided polygon can be found by first dividing it into triangles from one vertex.
 

What is the sum of the interior angles of this polygon?

   degrees 
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`720\ text(degrees)`

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`text(Sum of interior angles)`

`= 4 xx 180`

`= 720\ text(degrees)`