A geometry problem by Fidel Simanjuntak

Geometry Level 2

Find the value of $x$ in term $a, b$ and $c$ .

x=a+b-c

x=a-b-c

x= c+a-b

x=b+c-a

x=a+b+c

2 solutions

Fidel Simanjuntak
Jul 23, 2016

$b-a=c-x$

$\boxed{x=c+a-b}$

Sam Bealing
Jul 24, 2016

Consider drawing a perpendicular line to the two parallel lines to the right of the points. This creates a $6$ sided shapes whose angles add up to:

$180(6-2)=720°$

The angles also add up to:

$a+(360°-b)+c+(180-x)+90+90=720°+a-b+c-x$

$720°+a-b+c-x=720° \implies \boxed{\boxed{x=a+c-b}}$