The angles of a heptagon are $(x - 5) °, (x + 3) °, (5 x - 6) °, (2 x + 5) °, (x + 8) °, (2 x + 9) ° a n d (3 x + 1) °$ . The value of $x$ is

$59$

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$58$

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$60$

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$61$

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Solution

The correct option is A
$59$

As we know that the sum of measures of interior angles of a polygon having $n$ sides is $= (n - 2) \times 180 d e g r e e s$
So for heptagon $= (7 - 2) \times 180 ° = 900 °$
Now
$(x + 3) ° + (2 x + 5) ° + (x + 8) ° + (3 x + 1) ° + (5 x - 6) ° + (2 x + 9) ° + (x - 5) ° = 900 ° 15 x + 15 = 900 ° x = \frac{885}{15} = 59 °$
Hence, $x = 59 °$ .

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