Q24 of 24 Page 16

PQRSTU is a regular hexagon, Determine each angle of ΔPQT.

The sum of interior angles of a polygon = (n – 2) × 180°


The sum of interior angles of a hexagon = (6 – 2) × 180° = 4 × 180° = 720°


Measure of each angle of hexagon =


Proved above



In Δ PUT


[Angle sum property of a triangle]


[Since ΔPUT is isosceles triangle]





Similarly


Therefore





[Using angle sum property of triangle in ΔPQT]


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20

The measure of angles of a hexagon are x°, (x-5)°, (x-5)°, (2x-5)°, (2x-5)°, (2x+20)°. Find value of x.

 21

In a convex hexagon, prove that the sum of all interior angle is equal to twice the sum of its exterior angles formed by producing the sides in the same order.

 22

The sum of the interior angles of a polygon is three times the sum of its exterior angles. Determine the number of sides of the polygon.

 23

Determine the number of sides of a polygon whose exterior and interior angles are in the ratio 1 : 5.