Consider the pentagon below:

a

What is the interior angle sum of a pentagon?

b

Find an expression for the interior angle sum of the pentagon involving the exterior angles $v$`v`, $w$`w`, $x$`x`, $y$`y` and $z$`z`

c

Hence solve for the sum of the exterior angles of the pentagon. That is, solve for the value of $v+w+x+y+z$`v`+`w`+`x`+`y`+`z`.

d

Is the sum of exterior angles of any polygon equal to 360°?

Yes

A

No

B

Yes

A

No

B

Easy

Approx 8 minutes

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Determine, through investigation using a variety of tools and describe the properties and relationships of the interior and exterior angles of triangles, quadrilaterals, and other polygons, and apply the results to problems involving the angles of polygons

Determine, through investigation using a variety of tools and describe some properties of polygons, and apply the results in problem solving