Question

The angles of a pentagon are in the ratio $4:8:6:4:5$. Find each angle of the pentagon.

• A. ${40}^{\circ },{160}^{\circ },{120}^{\circ },{80}^{\circ }and{100}^{\circ }$
• B. ${60}^{\circ },{160}^{\circ },{120}^{\circ },{80}^{\circ }and{100}^{\circ }$
• C. ${80}^{\circ },{160}^{\circ },{120}^{\circ },{80}^{\circ }and{100}^{\circ }$
• D. ${30}^{\circ },{160}^{\circ },{120}^{\circ },{80}^{\circ }and{100}^{\circ }$

Answer 1

The correct option is C ${80}^{\circ },{160}^{\circ },{120}^{\circ },{80}^{\circ }and{100}^{\circ }$

The angles of a pentagon are in the ratio $4:8:6:4:5.$
Let angle be $4x,8x,6x,4x$ and $5x$.
Sum of interior angle of a polygon = ${180}^o(n-2)$
Sum of interior angle of a pentagon = ${180}^o(5-2)={540}^o$
$=>4x+8x+6x+4x+5x={540}^o$
$=>27x={540}^o$
$=>x={20}^o$
Angles are ${80}^o,{160}^o,{120}^o,{80}^{o}and{100}^o.$