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Understanding Quadrilaterals
What is a regular polygon?
State the name of a regular polygon of
(i) 3 sides (ii) 4 sides (iii) 6 sides
Solution: A polygon is said to be a regularpolygon if
(a) The measures of its interior angels are equal, and
(b) The lengths of its sides are equal.
The name of a regular polygon having
(i) 3 sides is ‘equilateral-triangle’
(ii) 4 sides is ‘square’
(iii) 6 sides is ‘regular hexagon’
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What is the sum of the measures of the angles of a convex quadrilateral? Will this property hold if the quadrilateral is not convex? (Make a non-convex quadrilateral and try!)
Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that).
|
Figure |
|
|
|
|
|
Side |
3 |
4 |
5 |
6 |
|
Angle sum |
180° |
2 x 180° = (4 - 2) x 180° |
3 x 180° = (5 - 2) x 180° |
4 x 180° = (6 - 2) x 180° |
What can you say about the angle sum of a convex polygon with number of sides?
(a) 7 (b) 8 (c) 10 (d) n
What is a regular polygon?
State the name of a regular polygon of
(i) 3 sides (ii) 4 sides (iii) 6 sides
Find the angle measure x in the following figures. 
Find x in the following figures.
Find the measure of each exterior angle of a regular polygon of (i) 9 sides (ii) 15 sides
How many sides does a regular polygon have if the measure of an exterior angle is 24°?
How many sides does a regular polygon have if each of its interior angles is 165°?
Question 5. (a) Is it possible to have a regular polygon with measure of each exterior angle is 22°?
(b) Can it be an interior angle of a regular polygon? Why?
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