Eric Nicholas K's answer to Clarine Peh's Primary 6 Maths Geometry Singapore question.
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If you look carefully at the angles, there are three pairs of vertically opposite angles.
ACB = ECF
DCE = GCA
FCG = BCD
so ACB + DCE + FCG = ECF + GCA + BCD,
but these six angles enclose a point (360 degrees) so ACB + DCE + FCG = 180 degrees
(ECF _ GCA + BCD happens to also be 180 degrees)
Since the three triangles have a total of 540 degrees, the sum of the 6 wanted angles
= 540 - (ACB + DCE + FCG)
= 540 - 180
= 360 degrees
ACB = ECF
DCE = GCA
FCG = BCD
so ACB + DCE + FCG = ECF + GCA + BCD,
but these six angles enclose a point (360 degrees) so ACB + DCE + FCG = 180 degrees
(ECF _ GCA + BCD happens to also be 180 degrees)
Since the three triangles have a total of 540 degrees, the sum of the 6 wanted angles
= 540 - (ACB + DCE + FCG)
= 540 - 180
= 360 degrees
Date Posted:
5 years ago
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