Question

The angles of a hexagon are $x + {10^ \circ },2x + {20^ \circ },2x - {20^ \circ },3x - {50^ \circ },x + {40^ \circ }$ and $x + {20^ \circ }$. Find x.

Answer 1

Hint: Before attempting this question one should have prior knowledge about the properties of hexagon and also remember that the sum of all the interior angles of hexagon is equal to \[{720^ \circ }\], using these instructions you can approach the solution of the question.

Complete step by step answer:
According to the given information we have a hexagon with angles $x + {10^ \circ },2x + {20^ \circ },2x - {20^ \circ },3x - {50^ \circ },x + {40^ \circ }$ and$x + {20^ \circ }$
As we know that the hexagon has a property according to which the sum of all interior angles in hexagon is equal to \[{720^ \circ }\]
Therefore $x + {10^ \circ } + 2x + {20^ \circ } + 2x - {20^ \circ } + 3x - {50^ \circ } + x + {40^ \circ } + x + {20^ \circ } = {720^ \circ }$
$ \Rightarrow $$10x + 20 = {720^ \circ }$
$ \Rightarrow $$10x = {700^ \circ }$
$ \Rightarrow $$x = \dfrac{{{{700}^ \circ }}}{{10}}$
$ \Rightarrow $$x = {70^ \circ }$

Therefore the value of x is equal to ${70^ \circ }$.

Note: In the above question we used the property of hexagon which can be explained as the 2-D shape polygon which have 6 sides where dimensions of each sides are same these hexagon are named as regular hexagon the properties shown by the hexagon are such as the total numbers of diagonals formed in hexagon is equal to 9, the sum of the interior angles consist by the hexagon is equal to 720 such that the each angle have a value of ${120^ \circ }$ but only in regular hexagon, whereas the sum of all exterior angles possessed by the regular hexagon is equal to ${360^ \circ }$ here each angle is shows the value of ${60^ \circ }$.