Question

The angles of a heptagon are$(\mathrm{x}+3)°,(2\mathrm{x}+5)°,(\mathrm{x}+8)°,(3\mathrm{x}+1)°,(5\mathrm{x}-6)°,(2\mathrm{x}+9)°\mathrm{and}(\mathrm{x}-5)°$. Calculate $\mathrm{x}$.

Answer 1

Calculating the value of $\mathrm{x}$:

As we know that the sum of measures of interior angles of a polygon having $n$ sides is$=(\mathrm{n}-2)\times 180\mathrm{degrees}$

As heptagon has $7$ sides.

So, sum of interior angles of heptagon$=(7-2)\times 180°=900°$

According to the question,

$$\begin{gathered} (\mathrm{x}+3)°+(2\mathrm{x}+5)°+(\mathrm{x}+8)°+(3\mathrm{x}+1)°+(5\mathrm{x}-6)°+(2\mathrm{x}+9)°+(\mathrm{x}-5)°=900° \\ \Rightarrow 15\mathrm{x}+15°=900° \\ \Rightarrow \mathrm{x}=\frac{885°}{15} \\ \Rightarrow \mathrm{x}=59° \end{gathered}$$

Hence, $x=59°$.