Short Answer TypeGiven here are some figures. 
Classify each of them on the basis of the following.
(a) Simple curve
(b) Simple closed curve
(c) Polygon
(d) Convex polygon
(e) Concave polygon
How many diagonals does each of the following have?
(a) A convex quadrilateral
(b) A regular hexagon
(c) A triangle
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
Solution: From the above table, we conclude that sum of the interior angles of polygon with n-sides = (n - 2) x 180°
(a) When n = 7
Substituting n = 7 in the above formula, we have Sum of interior angles of a polygon of 7 sides (i.e. when n = 7)
= (n - 2) x 180° = (7 - 2) x 180°
= 5 x 180°
= 900°
(b) When n = 8
Substituting n = 8 in the above formula, we have
Sum of interior angles of a polygon having 8 sides
= (n - 2) x 180° = (8 - 2) x 180°
= 6 x 180°
= 1080°
(c) When n = 10
Substituting n = 10 in the above formula, we have
Sum of interior angles of a polygon having 10 sides
= (n - 2) x 180° = (10 - 2) x 180°
= 8 x 180°
= 1440°
(d) When n = n
The sum of interior angles of a polygon having n-sides = (n - 2) x 180°
What is a regular polygon?
State the name of a regular polygon of
(i) 3 sides (ii) 4 sides (iii) 6 sides
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°?
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