GEOMETRY

Some Important points of Polygon
1. Sum of interior angle and exterior angle on the same vertex is 180^o.
2. Sum of all exterior angles is 360^o.
3. Sum of all interior angles is (n − 2) × 180^o
(n = no. of sides)
4. Number of diagonals in a polygon = 

Model Questions
1. Two angles are complementary to each other. If the first one is 70% more than the second one. Find difference between them.

Sol: Let the angles be a and b
a + b = 180^o

^{9. A regular polygon has 6 sides and the length of each side is 3 cm, find its area.}

^{10. There are 9 diagonals in a regular polygon. Find the number of interior angles.
A) 6        B) 12         C) 18           D) 4
Sol: Total number of diagonals = 9}
 = 9 [n = no. of sides]
n² - 3n = 18
n² - 3n - 18 = 0
n = 6
Number of interior angles = No. of sides = 6      Ans: A

11. Find the ratio of the measure of an interior angle of a regular pentagon to its exterior angle.
A) 2 : 3        B) 4 : 5        C) 5 : 4       D) 3 : 2
Sol: Interior angle : Exterior angle = (n - 2) : 2
= (5 - 2) : 2 [n = 5 for pentagon]
= 3 : 2                       Ans: D

12. Sum of all interior angles of a regular polygon is 540^o. Find the number of diagonals.
A) 5      B) 6      C) 9          D) 18
Sol: Sum of all interior angles = (n - 2) × 180^o
⇒ 540° = (n - 2) × 180^o
⇒ n - 2 = 3 ⇒ n = 5

13. Ratio of n interior angles to n exterior angles of a regular hexagon is 9 : 2. Find the number of interior angles.
A) 11      B) 20        C) 7         D) 9
Sol: Interior angle : Exterior angle = 9 : 2