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Sia 🤖 3 days, 18 hours ago

a = 120

^{0}, d = 5^{0}{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}

0Thank You