What is the value of x?

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Answer 1 · 2016-10-02T08:16:02

Seventh angle is $x = 111^{o}$ $x=111^o$

Sum of all the interior angles of a $n$ $n$ -sided polygon is always $(n - 2) \times 180^{o}$ $(n-2)xx180^o$ .

As this is seven sided polygon, sum of its interior angles is $(7 - 2) \times 180^{o} = 5 \times 180^{o} = 900^{o}$ $(7-2)xx180^o=5xx180^o=900^o$

Sum of six of the angles is $120^{o} + 158^{o} + 126^{o} + 125^{o} + 121^{o} + 139^{o} = 789^{o}$ $120^o +158^o +126^o +125^o +121^o +139^o =789^o$

Hence the seventh angle is $x = 900^{o} - 789^{o} = 111^{o}$ $x=900^o-789^o=111^o$

Answer 2 · 2016-10-02T08:21:39

$111^{\circ}$ $111^circ$

We use the formula

The sum of the angles in any closed polygon

$(n - 2) \cdot 180$ $color(blue)((n-2)*180)$

Where, $n$ $color(red)(n$ is the number of sides of the polygon

There are $7$ $7$ sides in this polygon

$:.$ $color(orange)("Sum of the angles"=(7-2)*180=900^circ$

So, we can say that

$rarr158^circ+120^circ+139^circ+121^circ+125^circ+126^circ+x=900^circ$

$rarr789^circ+x=900^circ$

$rarrx=900^circ-789^circ$

$rArrcolor(green)(x=111^circ$