When is a STAR confusing?

Geometry Level 1

Find the sum of all the interior angles of the 5 pointed star.

In other words, find the value of: a + b + c + d + e


The answer is 180.

A Former Brilliant Member by A Former Brilliant Member

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2 solutions

Shubham Nain
Aug 3, 2014

a+d+y=180,
a+c+p=180,
b+d+z=180,
e+b+q=180,
e+c+x=180,
2(a+b+c+d+e)+p+q+x+y+z=900,
2(a+b+c+d+e)=900-540,
a+b+c+d+e=180


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You should mention prom where p+q+x+y+z=540 came from that is it is the sum of interior angles of regular Pentagon.

Shounak Ghosh - 6 years, 10 months ago
Fares Salem
Aug 4, 2014

the sum of angles of the pentagon is 540, So one angle will be 108 because its a regular pentagon. the five triangles are isosceles because they are the arms of a star. so the angle of one of its base angles is 180-108= 72 Therefore the angle of the vertex of the triangle is 180-(72+72)=36 Therefore the angles a, b, c, d & e are equal to 36 degrees therefore the sum of them are 36*5=180 degrees

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The pentagon can be irregular.

Pedro Menéndez - 6 years, 10 months ago

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