Question

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

• A. ${120}^{\circ }$
• B. ${140}^{\circ }$
• C. ${160}^{\circ }$
• D. ${150}^{\circ }$

Answer 1

Answer: (C)

${160}^{\circ }$

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

Let angle be $4x,8x,6x,4xand5x$.

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 ${80}^o,{160}^o,{120}^o,{80}^{o}and{100}^o.$