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.
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
Find the sum of integers from 1 to 100 that are divisible by 2 or 5.
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How many terms of G.P. 3, 32, 33, … are needed to give the sum 120?
Find the sum of all numbers between 200 and 400 which are divisible by 7.
Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.
Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.
A coin is tossed 3 times and the outcomes are recorded. How many possible outcomes are there?
Find the sum to n terms in the geometric progression 1,-a, a2,-a3, ... (if a ≠ -1)
A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?
A die is thrown. Describe the following events:
(i) A: a number less than 7 (ii) B: a number greater than 7 (iii) C: a multiple of 3
(iv) D: a number less than 4 (v) E: an even number greater than 4 (vi) F: a number not less than 3
Also find A ∪ B, A ∩ B, B ∪ C, E ∩ F, D ∩ E, A – C, D – E, E ∩ F’, F’
Name the octants in which the following points lie:
(1, 2, 3), (4, –2, 3), (4, –2, –5), (4, 2, –5), (–4, 2, –5), (–4, 2, 5), (–3, –1, 6), (2, –4, –7)
If the 4th, 10th and 16th terms of a G.P. are x, y and z, respectively. Prove that x, y, z are in G.P.
The numbers 1, 2, 3 and 4 are written separately on four slips of paper. The slips are put in a box and mixed thoroughly. A person draws two slips from the box, one after the other, without replacement. Describe the sample space for the experiment.
Find the sum of integers from 1 to 100 that are divisible by 2 or 5.
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 5°. Could you please explain?
Here difference between 16 and 9 is seven. So rejected the value of n=16. So number of sides of polygon is 9.
Here first and last angles are also consecutive, but difference is more than 5.