Question 18

The difference between any two consecutive interior angles of a polygon is 5°. If the smallest angle is 120°, find the number of the sides of the polygon.

Answer

The angles of the polygon will form an A.P. with common difference *d* as 5° and first term *a* as 120°.

It is known that the sum of all angles of a polygon with *n* sides is 180° (*n* – 2).

So

- Q:-
Find the sum of integers from 1 to 100 that are divisible by 2 or 5.

- Q:-
If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.

- Q:-
A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?

- Q:- Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.
- Q:-
The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms.

- Q:-
How many terms of G.P. 3, 3

^{2}, 3^{3}, … are needed to give the sum 120? - Q:-
Find the sum of all numbers between 200 and 400 which are divisible by 7.

- Q:- Write the following sets in roster form:

(i) A = {x: x is an integer and - 3 < x < 7}.

(ii) B = {x: x is a natural number less than 6}.

(iii) C = {x: x is a two-digit natural number such that the sum of its digits is 8}

(iv) D = {x: x is a prime number which is divisor of 60}.

(v) E = The set of all letters in the word TRIGONOMETRY.

(vi) F = The set of all letters in the word BETTER. - Q:-
Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.

- Q:-
Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.

- Q:-
The sum of first three terms of a G.P. is 16 and the sum of the next three terms is 128. Determine the first term, the common ratio and the sum to

*n*terms of the G.P. - Q:-
Find the sum to

*n*terms of the series 3 × 8 + 6 × 11 + 9 × 14 +… - Q:-
The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms.

- Q:-
Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.

- Q:- Write the following sets in the set-builder form:

(i) (3, 6, 9, 12)

(ii) {2, 4, 8, 16, 32}

(iii) {5, 25, 125, 625}

(iv) {2, 4, 6 upto infinity}

(v) {1, 4, 9, upto 100} - Q:-
Find the sum to

*n*terms of the series 1 × 2 × 3 + 2 × 3 × 4 + 3 × 4 × 5 + … - Q:-
A die is thrown repeatedly until a six comes up. What is the sample space for this experiment?

- Q:-
Prove the following by using the principle of mathematical induction for all n ∈ N:

n (n + 1) (n + 5) is a multiple of 3.

- Q:-
If the sum of

*n*terms of an A.P. is 3n^{2}+ 5n and its*m*th term is 164, find the value of*m*. - Q:-
A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?

VERISHA COLTON
2019-01-17 20:57:15

They say that the difference between ANY two consecutive angles. So it could be the last and the first one as well but then like Lalit Mohan said the difference is more than 5Â°. Could you please explain?

Simran
2017-09-06 06:28:39

Here difference between 16 and 9 is seven. So rejected the value of n=16. So number of sides of polygon is 9.

LALIT MOHAN SAINI
2015-11-23 13:41:56

Here first and last angles are also consecutive, but difference is more than 5.

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