Question

If the interior angles of a pentagen measure $x^{\circ },(x-10{)}^{\circ },(x+20{)}^{\circ },(2x-44{)}^{\circ }$ and $(2x-70{)}^{\circ }$, then x = ___ .

• A. ${92}^{\circ }$
• B. ${90}^{\circ }$
• C. ${82}^{\circ }$
• D. ${80}^{\circ }$

Answer 1

The correct option is A

${92}^{\circ }$

Sum of interior angles of a n sided polygon = (2n - 4) x 90°

A pentagon has 5 sides.

Sum of interior angles of a pentagon $=(10-4)\times {90}^{\circ }$

$x+x-10+x+20+2x-44+2x-70=6\left({90}^{\circ }\right)$

$7x-104={540}^{\circ }$

$7x$ = 644

$x$ = 92°