Question
Is it possible to have a polygon whose sum of interior angles is $7$ right angles?
✓
Answer
Let the number of sides in the polygon be $n$.
$\therefore( n -2) \times 180^{\circ}=7 $ Right Angles
$\Rightarrow( n -2) \times 180^{\circ}=7 \times 90^{\circ} $
$\Rightarrow 180^{\circ} n -360^{\circ}=630^{\circ} $
$\Rightarrow 180^{\circ} n =990^{\circ} $
$\Rightarrow n =\frac{990^{\circ}}{180^{\circ}} $
$=\frac{11}{2} $
$=5 \frac{1}{2}$
Since the number of sides of a polygon cannot be in a fraction,
therefore the polygon is not possible.
$\therefore( n -2) \times 180^{\circ}=7 $ Right Angles
$\Rightarrow( n -2) \times 180^{\circ}=7 \times 90^{\circ} $
$\Rightarrow 180^{\circ} n -360^{\circ}=630^{\circ} $
$\Rightarrow 180^{\circ} n =990^{\circ} $
$\Rightarrow n =\frac{990^{\circ}}{180^{\circ}} $
$=\frac{11}{2} $
$=5 \frac{1}{2}$
Since the number of sides of a polygon cannot be in a fraction,
therefore the polygon is not possible.
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