# A polyhedron has 7 faces and 15 edges. How many vertices does this polyhedron have?

$AccordingtoEuler\text{'}sTheorem,inanysolidshape,\phantom{\rule{0ex}{0ex}}Faces+Vertices-Edges=2\phantom{\rule{0ex}{0ex}}\Rightarrow 7+Vertices-15=2\phantom{\rule{0ex}{0ex}}\Rightarrow Vertices=10\phantom{\rule{0ex}{0ex}}Thus,thepolyhedronhas10vertices.$

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