document.write( "Question 62347: please help me slove this proof problem ---> \"Prove that the exterior vertex angel is congruent to the central angle of a regular ploygon. [using congruence and or equal angle measure relationships, not by formula] \n" ); document.write( "
Algebra.Com's Answer #43237 by venugopalramana(3286)\"\" \"About 
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please help me slove this proof problem ---> \"Prove that the exterior vertex angel is congruent to the central angle of a regular ploygon. [using congruence and or equal angle measure relationships, not by formula]
\n" ); document.write( "IN A REGULAR POLYGON ALL SIDES ARE EQUAL.ALL INTERNAL ANGLES ARE SAME.TAKE ANY 2 ADJACENT SIDES AB AND BC.LET O BE THE CENTRE OF THE POLYGON.JOIN OA,OB AND OC.
\n" ); document.write( "OA=OB=OC.......ANGLE
\n" ); document.write( "HENCE IN TRIANGLES OAB AND OBC,
\n" ); document.write( "OB = OB
\n" ); document.write( "OA = OC
\n" ); document.write( "AB = BC
\n" ); document.write( "HENCE THE 2 TRIANGLES ARE CONGRUENT.
\n" ); document.write( "ANGLE OBA= ANGLE OBC = X SAY.................1
\n" ); document.write( "SO ANGLE ABC = ANGLE ABO + ANGLE OBC = 2X........2
\n" ); document.write( "SINCE OA=OB
\n" ); document.write( "ANGLE OAB = ANGLE OBA = X .....................3
\n" ); document.write( "HENCE VERTEX ANGLE = ANGLE AOB = 180 - ANGLE OBA - ANGLE OAB = 180-2X......4
\n" ); document.write( "IF AB IS EXTENDED TO Z THEN
\n" ); document.write( "ANGLE OBZ IS THE EXTERNAL ANGLE IN TRIANGLE OAB = SUM OF OPPOSITE INTERNAL ANGLES = ANGLE OAB + ANGLE OBA = X + 180 - 2X = 180 - X.
\n" ); document.write( "EXTERNAL ANGLE OF POLYGON = ANGLE CBZ = ANLE OBZ - ANGLE OBC
\n" ); document.write( "= 180 - X - X = 180 - 2X = VERTEX ANGLE OF POLYGON. \n" ); document.write( "
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