Geometry

NZ Level 5

Interior and Exterior Angles of Polygons

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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Deduce the angle properties of intersecting and parallel lines and the angle properties of polygons and apply these properties