Chapter 11.2, Problem 21IP

To determine

To find: The value of $x$ .

Answer to Problem 21IP

  $x={53}^0$

Explanation of Solution

Given information:

Exterior angle $={108}^0$

Opposite interior angles are $x^0$ and ${\left(x+2\right)}^0$

Given

Exterior angle $={108}^0$

Opposite interior angles are $x^0$ and ${\left(x+2\right)}^0$

We know exterior angle is equal to sum of opposite interior angles

Using that

We get

  $x+\left(x+2\right)={108}^0$

On solving

  $\begin{array}{l}x+\left(x+2\right)={108}^0\\ \Rightarrow x+x+2^0={108}^0\\ \Rightarrow 2x+2^0={108}^0\\ \Rightarrow 2x={108}^0-2^0\\ \Rightarrow 2x={106}^0\\ \Rightarrow x=\frac{{106}^0}{2}\\ \Rightarrow x={53}^0\end{array}$

Therefore,

  $x={53}^0$