Question

The angles of a pentagon are $3x+4^o,x+{20}^o,3x-5^o,2x+{10}^o$ and $4x-9^o$. Find ${}^{\prime }{x}^{\prime }$ (in degrees)

• A. ${40}^o$
• B. ${50}^o$
• C. ${45}^o$
• D. none of the above

Answer 1

Answer: (A)

${40}^o$

Given the angles of a Pentagon are as follows:

$3x+4^o,x+{20}^o,3x-5^o,2x+{10}^o$ and $4x-9^o$

We know that Sum of interior angles of a Pentagon

$=(5-2)\times {180}^o=3\times {180}^o={540}^o(3x+4^o)+(x+{20}^o)+(3x-5^o)+(2x+{10}^o)+(4x-9^o)={540}^o\Rightarrow 3x+x+3x+2x+4x+4^o+{20}^o-5^o+{10}^o-9^o={540}^o\Rightarrow 13x+{20}^o={540}^o\Rightarrow 13x={540}^o-{20}^o\Rightarrow 13x={520}^o\Rightarrow x=\frac{{520}^o}{13}={40}^o$

Therefore value of $x$ $={40}^o$