The measure of an interior angle of a regular polygon is 162o. Find the number of sides of the polygon.
20
The exterior angle of a regular polygon is supplementary to the interior angle: \(180^\circ - 162^\circ = 18^\circ\).
The sum of all exterior angles of any polygon is \(360^\circ\), so the number of sides is \(n = \dfrac{360^\circ}{18^\circ} = 20\).
Hence, the polygon has 20 sides.
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Important Questions from Geometry
ABCDEF is a regular hexagon. Side of the hexagon is 36 cm. What is the area of the triangle AOB ?
If ∆ABC ~ ∆DEF, and BC = 4 cm, EF = 5 cm and the area of triangle ABC = 80 cm 2, then the area of the triangle DEF is:
If Δ ABC is right angled at B, AB = 12 cm and ∠CAB = 60°, determine the length of BC.
If ΔABC and ΔDEF are congruent triangles, then which of the following is FALSE?
D and E are points on the sides AB and AC, respectively, of ΔABC such that DE is parallel to BC and AD ∶ DB = 7 ∶ 9. If CD and BE intersect each other at F. then find the ratio of areas of ΔDEF and ΔCBF.
