Question

What is the value of x?

Answer 1

Seventh angle is `x=111^o`

Explanation:

Sum of all the interior angles of a `n`-sided polygon is always `(n-2)xx180^o`.

As this is seven sided polygon, sum of its interior angles is `(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`

Hence the seventh angle is `x=900^o-789^o=111^o`

Answer 2

`111^circ`

Explanation:

We use the formula

The sum of the angles in any closed polygon

`color(blue)((n-2)*180)`

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

There are `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`