March 13, 2017 ISLAMIYA ENGLISH SCHOOL, ABU DHABI.

GRADE: 8 POLYGONS CHAPTER: 15

NOTE:

Any plane closed figure bounded by straight lines is called a polygon. A convex polygon has no interior angle greater than 180°. A regular polygon has all of its sides and all of its angles equal. A pentagon is a polygon with 5 sides. A hexagon is a polygon with 6 sides. An octagon is a polygon with 8 sides. In a convex polygon having n sides the sum of the interior angles is (2n−4 ) right

angles. i.e. (2n−4 )90 °. The sum of the exterior angles is 360°, no matter how many sides the polygon has. The above two statements apply to all polygons not just regular polygons.

Each exterior angle is equal to 360° divided by number of sides. Extr∠=360 °n .

Sum of exterior angle and interior angle is 180°.

Interior angle ¿(2n−4 )90 °

n .

1. Find the sum of the interior angles of a convex polygon with:(a) 5 (b) 8 (c) 10 (d) 12 sides.

2. If the polygons are regular find the size of interior angle of each having (a) 5 (b) 6 (c) 8 (d) 10 sides.

3. Find the size of each exterior angle of a regular polygon with:(a) 8 (b) 9 (c) 15 (d) 18 sides.

4. Find the number of sides of a polygon if each exterior angle is:(a) 72° (b) 45° (c) 22.5° (d) 15°.

5. Each interior angle of a regular polygon is 150°. Find the number of sides of this polygon.6. The exterior angles of a regular polygon are each 45°. Find the number of sides of the polygon.7. Each interior angle of a regular polygon is 165°. Find the number of sides of this polygon.8. The exterior angles of a regular polygon are each 15°. Calculate the number of sides of the

polygon.9. Calculate the size of an interior angle of a regular 20-sided polygon.10. A regular polygon has 32 sides. Calculate the size of each interior angle.11. Calculate the size, in degrees, of an exterior angle of a regular 12-sided polygon.12. The exterior angles of a hexagon are x ,2 x ,3 x ,4 x ,3 x and 2 x. Find the value of x.13. A quadrilateral has 110° ,2x , x ,2x as exterior angles. What is the value of x?14. The interior angles of a pentagon are x ,120 ° ,90° ,110° , x . Find the size of the angle x.15. In a regular polygon each interior angle is greater by 150° than each exterior angle. Calculate the

number of sides of the polygon.

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MS.SARVATH FATHIMA. 1