If \(x\) represents the sum of the interior angles of a

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AAPL: Moderator; Posts: 2599; Joined: Sun Oct 29, 2017 2:08 pm; Followed by:2 members

If \(x\) represents the sum of the interior angles of a

by AAPL » Wed Jun 26, 2019 6:03 am

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If \(x\) represents the sum of the interior angles of a regular hexagon and y represents the sum of the interior angles of a regular pentagon, then the difference between \(x\) and \(y\) is equal to the sum of the interior angles of what geometric shape?

A. Triangle
B. Square
C. Rhombus
D. Trapezoid
E. Pentagon

OA A

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Source: Beat The GMAT — Problem Solving | Wed Jun 26, 2019 6:03 am

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by Scott@TargetTestPrep » Mon Jul 01, 2019 4:09 pm

AAPL wrote:Manhattan Prep

If \(x\) represents the sum of the interior angles of a regular hexagon and y represents the sum of the interior angles of a regular pentagon, then the difference between \(x\) and \(y\) is equal to the sum of the interior angles of what geometric shape?

A. Triangle
B. Square
C. Rhombus
D. Trapezoid
E. Pentagon

OA A

The formula for the sum of the interior angles of an n-gon (a polygon with n sides) is 180 (n - 2).

The sum of the interior angles of a regular hexagon (n = 6) is 180(6 - 2) = 180 x 4 = 720.

The sum of the interior angles of a regular pentagon (n = 5) is 180(5 - 2) = 180 x 3 = 540.

So the difference is 180, which is the sum of the interior angles of a triangle.

Answer: A

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