Question

Two angles of an eight sided polygon are ${142}^{\circ }$and ${176}^{\circ }$. If the remaining angles are equal to each other; find the magnitude of each of the equal angles.

• A. ${156}^{\circ }$
• B. ${127}^{\circ }$
• C. ${136}^{\circ }$
• D. ${116}^{\circ }$

Answer 1

Answer: (B)

${127}^{\circ }$

Two angles of an eight sided polygon are ${142}^o$ and ${176}^o$ and the remaining angles are equal to each other. Let each equal angle $=x$
Sum of all interior angles of a polygon is = ${180}^o(n-2)={180}^o(8-2)={1080}^o$
Now,
${142}^o+{176}^o+(8-2)\times x={1080}^o$
$⟹6x=762$

$⟹x={127}^o$

Each equal angle = ${127}^o$