In a parallelogram A B C D AB is 7.2 cm and the perpendicular from C on AB is 4.5 cm find area of parallelogram ABCD
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Home » Forum » Algebrnterior angles of a polygon are in...
The interior angles of a polygon are in arithmetic progression. The smallest angle is 120°, and the common difference is 5°, Find the number of sides of the polygon.
4 years ago
Answers : (2)
Hello Student,
Please find the answer to your question
Let there be in n sides in the polygon.
Then by geometry, sum of all n interior angles of polygon = (n – 2) * 180°
Also the angles are in A. P. with the smallest angle = 120° , common difference = 5°
∴ Sum of all interior angles of polygon
= n/2[2 * 120 + ( n – 1) * 5
Thus we should have
n/2 [2 * 120 + (n – 1) * 5] = (n – 2) * 180
⇒ n/2 [5n + 235] = (n – 2 ) * 180
⇒ 5n2 + 235n = 360n – 720
⇒ 5n2 – 125n + 720 = 0 ⇒ n2 – 25n + 144 = 0
⇒ (n – 16 ) (n – 9) = 0 ⇒ n = 16, 9
Also if n = 16 then 16th angle = 120 + 15 * 5 = 195° > 180°
∴ not possible.
Hence n = 9.
Thanks
Aditi Chauhan
askIITians Faculty
4 years ago Smallest angle=120degreeCommon difference=5A P is 120, 125, 130,……..The sum of interior angles of a polygon= (n-2)180Hence Sum of n terms of an A P = (n-2)180n/2 {2.120+(n-1)5} = 180(n-2)5n^2 -125n +720 = 0n^2 -25n +144=0n=9 or 16hence number of sides can be 9 or 16 one year ago
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Home » Forum » Algebra » The interior angles of a polygon are in...
The interior angles of a polygon are in arithmetic progression. The smallest angle is 120°, and the common difference is 5°, Find the number of sides of the polygon.
4 years ago
Answers : (2)
Hello Student,
Please find the answer to your question
Let there be in n sides in the polygon.
Then by geometry, sum of all n interior angles of polygon = (n – 2) * 180°
Also the angles are in A. P. with the smallest angle = 120° , common difference = 5°
∴ Sum of all interior angles of polygon
= n/2[2 * 120 + ( n – 1) * 5
Thus we should have
n/2 [2 * 120 + (n – 1) * 5] = (n – 2) * 180
⇒ n/2 [5n + 235] = (n – 2 ) * 180
⇒ 5n2 + 235n = 360n – 720
⇒ 5n2 – 125n + 720 = 0 ⇒ n2 – 25n + 144 = 0
⇒ (n – 16 ) (n – 9) = 0 ⇒ n = 16, 9
Also if n = 16 then 16th angle = 120 + 15 * 5 = 195° > 180°
∴ not possible.
Hence n = 9.
Thanks
Aditi Chauhan
askIITians Faculty
4 years ago Smallest angle=120degreeCommon difference=5A P is 120, 125, 130,……..The sum of interior angles of a polygon= (n-2)180Hence Sum of n terms of an A P = (n-2)180n/2 {2.120+(n-1)5} = 180(n-2)5n^2 -125n +720 = 0n^2 -25n +144=0n=9 or 16hence number of sides can be 9 or 16 one year ago
Think You Can Provide A
Better Answer ?
Answer & Earn Cool Goodies
Other Related Questions on Algebra
1/n+1 + 1/n+2 +.....+ 1/2n > 13/24 , n = 2,3,4,.....
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Complete JEE Main/Advanced Course and Test Series
OFFERED PRICE: Rs. 15,900
View Details Xpress Buy
Course Features
731 Video LecturesRevision NotesPrevious Year PapersMind MapStudy PlannerNCERT SolutionsDiscussion ForumTest paper with Video Solution
Ask Experts
Have any Question? Ask Experts
Answer ‘n’ Earn Attractive Gift
Vouchers To Win!!!
Click Here for details
More Links »
copyright © 2006-2019 askIITians.com