If the interior angles of a pentagon are (3x + 4)°, (x + 20)°, (3x - 5)°, (2x + 10)° and (4x - 9)°, then x is equal to

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Solution

Sum of the interior angles of a pentagon = $540^{\circ}$

$\Rightarrow (3 x + 4) ° + (x + 20) ° + (3 x - 5) ° + (2 x + 10) ° + (4 x - 9) ° = 540^{\circ}$

$\Rightarrow 13 x + 20^{\circ} = 540^{\circ}$

$\Rightarrow 13 x = 540^{\circ} - 20^{\circ}$

$\Rightarrow x = \frac{520}{13}$

$\Rightarrow x = 40^{\circ}$

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