Question

The four angles of a pentagon are ${40}^{\circ },{75}^{\circ },{125}^{\circ },$ and ${135}^{\circ }$ respectively. Find the fifth angle.

Answer 1

Suppose fifth angle be $x^{\circ }$
Since, in a pentagon, the sum of all interior angles equals to ${540}^{\circ }$
$(x+40{)}^{\circ }+{75}^{\circ }+{125}^{\circ }+{135}^{\circ }={540}^{\circ }$
$\Rightarrow x+375=540$
$\Rightarrow x=540–375$
$\therefore x={165}^{\circ }$