What is the value of x?

Oct 2, 2016

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

Explanation:

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

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

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

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

Oct 2, 2016

${111}^{\circ}$

Explanation:

We use the formula

The sum of the angles in any closed polygon

$\textcolor{b l u e}{\left(n - 2\right) \cdot 180}$

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

There are $7$ sides in this polygon

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

So, we can say that

$\rightarrow {158}^{\circ} + {120}^{\circ} + {139}^{\circ} + {121}^{\circ} + {125}^{\circ} + {126}^{\circ} + x = {900}^{\circ}$

$\rightarrow {789}^{\circ} + x = {900}^{\circ}$

$\rightarrow x = {900}^{\circ} - {789}^{\circ}$

rArrcolor(green)(x=111^circ