Starry Pentagon

Geometry Level 1

In the image below, equilateral triangles, shown in green, are placed along each edge of a regular pentagon, shown in blue. What is the sum of the measures of the red angles?

36 0 ∘ 360^\circ 24 0 ∘ 240^\circ 12 0 ∘ 120^\circ 6 0 ∘ 60^\circ

Janae Pritchett by Janae Pritchett

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

David Vreken
Jul 30, 2018

The outer pentagon has an interior angle sum of ( 5 − 2 ) 180 ° = 540 ° (5 - 2)180° = 540° , and each of the 5 5 equilateral triangles have interior angles of 60 ° 60° .

The sum of the measures of the red angles is therefore 540 ° − 5 ⋅ 60 ° = 240 ° 540° - 5 \cdot 60° = \boxed{240°} .

4 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...