Question

Five angles of a hexagon have measures ${100}^{\circ },{110}^{\circ },{120}^{\circ },{130}^{\circ }$ and ${140}^{\circ }$. What is the measure of the remaining angle?

Answer 1

Number of sides in a hexagon$=n=6$

Sum of interior angles$=(n-2){180}^{\circ }=(6-2){180}^{\circ }={720}^{\circ }$

Let the remaining angle be $x$

$\Rightarrow x+{100}^{\circ }+{120}^{\circ }+{130}^{\circ }+{140}^{\circ }={720}^{\circ }$

$\Rightarrow x+{600}^{\circ }={720}^{\circ }$

$\Rightarrow x={720}^{\circ }-{600}^{\circ }={120}^{\circ }$

$\therefore$ Measure of sixth angle is ${120}^{\circ }$