Question

One angle of a six-sided polygon is ${140}^{\circ }$ and the other angles are equal. Find the measure of each equal angle.

• A. ${116}^{\circ }$
• B. ${126}^{\circ }$
• C. ${112}^{\circ }$
• D. ${118}^{\circ }$

Answer 1

The correct option is A ${116}^{\circ }$

One angle of a six-sided polygon is ${140}^o$ and the other angles are equal.
n = 6
Sum of interior angles of a polygon of 6 sides $=180(n-2)=180(6-2)=720$
=> ${140}^o+5\times x={720}^o$
=> $5\times x={580}^o$
=> $x={116}^o$
Each equal angle is ${116}^o$.