Question

The angles of a pentagon in degrees are x, x + 20, x + 40, x + 60 and x + 80, then the smallest angle of the pentagon is

• A. ${50}^o$
• B. ${68}^o$
• C. ${78}^o$
• D. ${85}^o$

Answer 1

Answer: (B)

${68}^o$

Given angle of pentagon are $x,x+20,x+40,x+60$ and $x+80$

We know that sum of angle of pentagon $={540}^0$

Then $x+x+20+x+40+x+60+x+80=540$

$\Rightarrow 5x+200=540$

$\Rightarrow 5x=540-200$

$\Rightarrow x=\frac{340}{5}={68}^o$

Then smallest angle of pentagon is ${68}^o$