$$? = N\,\,\left( {{\rm{number}}\,\,{\rm{of}}\,\,{\rm{sides}}\,\,{\rm{of}}\,\,{\rm{polygon}}\,\,M} \right)$$AAPL wrote:Veritas Prep
In the figure above, polygon M has been partially covered by a piece of paper. How many sides does M have?
1) x + y = 45
2) M is a regular polygon
All measures are in degrees.
Each statement alone is insufficient, as PROVEN by the Geometric Bifurcations shown below:
$$\left( {1 + 2} \right)\,\,\,\,\left\{ \matrix{
\,\left( 1 \right)\,\,\,\, \Rightarrow \,\,\,A = 180 - \left( {x + y} \right) = 135 \hfill \cr
\,\left( 2 \right)\,\,\,\, \Rightarrow \,\,A = {{\left( {N - 2} \right) \cdot 180} \over N} \hfill \cr} \right.\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,? = N = {\rm{unique}}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left( {\rm{C}} \right)$$
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
