- Three diagonals can be drawn from vertex O: OA, OB, OC.
ODand OEare not diagonals; they are sides. - 720°. Three diagonals can be drawn from vertex O, so there are
four triangles created. Therefore, the sum of the interior angles of
this 6-sided polygon is 180(4) = 720°.
Set 46
- Heptagon ORLMNPQ.As long as you list their vertices in
consecutive order, any one of these names will do: RLMNPQO,
MNPQOLR, NPQOLRM, PQOLRMN, QOLRMNP. Heptagon
ORLMNPQ is concave because vertex N exceeds 180°. - Four diagonals can be drawn from vertex O: OL, OM, ON,
OP. - 900°. Four diagonals can be drawn from vertex O, so there are five
triangles created. Therefore, the sum of the interior angles of this
7-sided polygon is 180(5) = 900°.
Set 47
- Octagon SUVWXOYZ.If you list every vertex in consecutive
order, then your name for the polygon given is correct. Also,
octagon SUVWXOYZ is concave.The measures of vertices U,
W, O and Z exceed 180°. - Five diagonals can be drawn from vertex O: OZ, OS, OU,
OV, OW. - 1080°. Five diagonals can be drawn from vertex O, so there are six
triangles created. Therefore, the sum of the interior angles of this
8-sided polygon is 180(6) = 1080°.
Set 48
- Nonagon HIJKLMNOP.List every vertex in consecutive order
and your answer is correct. Also, nongon HIJKLMNOP is
regular and convex.
501 Geometry Questions