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SAT Math: Geometry

Polygons

Screen Shot 2013-12-18 at 11.29.12 AM.jpg

If all angles in the polygon above are congruent, then a =
A.  20
B.  35
C.  60
D.  72
E.  120

Knowsys Method. 

Read the problem carefully.  The problem states that all angles in the polygon are congruent, which means that you can apply rules for regular polygons. 

Identify the bottom line.  a = ?

Assess your options.  There are two ways to find the total number of degrees in a regular polygon.  You can:

1) use the polygon rule:
     180 (n – 2 )
     n is the number of vertices

2) divide the polygon into triangles and multiply the number of triangles by 180 degrees  

We will demonstrate both methods below.  

Attack the problem.  Either use the polygon rule or divide the polygon into triangles to find the total number of degrees in the polygon.  

Screen Shot 2013-12-18 at 11.29.25 AM.jpg

Now, divide the total number of degrees in this polygon by the number of vertices to find the measure of each individual angle. 

Screen Shot 2013-12-18 at 11.29.37 AM.jpg

The interior angle and a are supplementary, so subtract 120 from 180 to get the value of a. 

180 – 120 = 60  

Loop back.  Did you find the value of a?  Yes.  a = 60, which is answer choice C.

The correct answer is C.

This is a medium level problem. 

Want some help reviewing the math concepts you need to master?  Try out the Knowsys Pre-Algebra Flashcards, the Knowsys Algebra I Flashcards, and the Knowsys SAT & ACT Math Practice book.  

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