The interior angles of a polygon ...

The interior angles of a polygon are in AP. The smallest angle is 120 and c. d. is 5. Find the no. of sides of polygon
  • 1 answers

Sia 🤖 3 days, 18 hours ago

a = 1200, d = 50
{tex}s _ { n } = \frac { n } { 2 } [ 2 a + ( n - 1 ) d ]{/tex}
{tex}s _ { n } = \frac { n } { 2 } [ 2 \times 120 + ( n - 1 ) 5 ]{/tex}
{tex}= \frac { n } { 2 } [ 240 + 5 n - 5 ]{/tex}
{tex}= \frac { n } { 2 } [ 235 + 5 n ]{/tex}
Also
sum of interior angles of a polygon with n sides = (2n - 4) {tex}\times{/tex} 90
ATQ {tex}\frac { n } { 2 } [ 235 + 5 n ] = ( 2 n - 4 ) \times 90{/tex}
n = 9, 16
but n = 16 not possible
n = 9
{tex}s _ { n } = \frac { n } { 2 } [ 2 a + ( n - 1 ) d ]{/tex}
{tex}s _ { n } = \frac { n } { 2 } [ 2 \times 120 + ( n - 1 ) 5 ]{/tex}
{tex}= \frac { n } { 2 } [ 240 + 5 n - 5 ]{/tex}
{tex}= \frac { n } { 2 } [ 235 + 5 n ]{/tex}
Also
Sum of interior angle of polygon with n sides {tex}= ( 2 \mathrm { n } - 4 ) \times 90{/tex}

Related Questions:

Find zeros
  • 5 answers
Ian not any I am anjela ok
  • 0 answers
Hello friends.....
  • 8 answers

Buy Complete Study Pack

Subscribe complete study pack and get unlimited access to selected subjects. Effective cost is only ₹ 12.5/- per subject per month. Based on the latest CBSE & NCERT syllabus.

myCBSEguide App

myCBSEguide

Trusted by 70 Lakh Students

CBSE Test Generator

Create papers in minutes

Print with your name & Logo

Download as PDF

3 Lakhs+ Questions

Solutions Included

Based on CBSE Blueprint

Best fit for Schools & Tutors

Work from Home

  • Work from home with us
  • Create questions or review them from home

No software required, no contract to sign. Simply apply as teacher, take eligibility test and start working with us. Required desktop or laptop with internet connection