9000121710
Level:
B
Consider a regular hexagon \(ABCDEF\)
with the center \(S\). Let the
point \(G\) be the middle
of the side \(DE\). Find the
measure of the angle \( BSG\).
\(150^{\circ }\)
\(160^{\circ }\)
\(135^{\circ }\)
\(120^{\circ }\)
Polygons
9000121801
Level:
B
Find the number of diagonals in the regular decagon (a regular polygon with
\(10\)
vertices).
\(35\)
\(7\)
\(10\)
\(70\)
9000121802
Level:
B
Consider a regular polygon with the central angle of
\(20^{\circ }\). In the figure the cut of a regular polygon with unspecified number of vertices is shown. The red angle is the central angle of the polygon. Find
the number of vertices of this polygon.
\(18\)
\(9\)
\(20\)
\(15\)
9000121803
Level:
B
Consider a regular polygon with the central angle of
\(24^{\circ }\). In the figure the cut of a regular polygon with unspecified number of vertices is shown. The red angle is the central angle of the polygon. Find
the number of diagonals in this polygon.
\(90\)
\(15\)
\(72\)
\(45\)
9000121804
Level:
B
Find the number of vertices of a regular polygon with
\(27\)
diagonals.
\(9\)
\(18\)
\(6\)
\(24\)
9000121805
Level:
B
For a regular pentagon find the interior angle. In the figure a regular pentagon with an interior angle marked in red is shown.
\(108\)
\(144\)
\(112\)
\(72\)
9000121806
Level:
B
The measure of the interior angle in a regular polygon is \(160^{\circ}\). Find the number of vertices of this polygon. In the figure the interior angle (marked in red) of a regular hexagon is shown.
\(18\)
\(16\)
\(32\)
\(9\)
9000121807
Level:
B
In the figure the cut of a regular polygon with unspecified number of vertices is shown. The red angle is the central angle of the polygon, the blue angle is the interior angle of the polygon. Suppose we consider a regular polygon with the central angle of \(40^{\circ}\), then find the measure of the interior angle of this polygon.
\(140^{\circ }\)
\(80^{\circ }\)
\(200^{\circ }\)
\(120^{\circ }\)
9000121808
Level:
B
The number of diagonals in a polygon is three times bigger than the number of sides
of this polygon. Find the number of vertices of this polygon.
\(9\)
\(12\)
\(6\)
\(15\)
9000121809
Level:
B
The number of diagonals in a regular polygon is
\(2.5\)-times bigger than the number of the sides of this polygon. In the figure the cut of a regular polygon with unspecified number of vertices is shown. The red angle is the central angle of the polygon. Find the central angle of the
polygon.
\(45^{\circ }\)
\(50^{\circ }\)
\(135^{\circ }\)
\(35^{\circ }\)