Chapter 1.2, Problem 28E

To determine

To determine the value of x .

Answer to Problem 28E

  $x={125}^{\circ }$

Explanation of Solution

Given:

  

Concept used:

The sum of interior angles is ${720}^{\circ }.$

Calculation:

  

From the above figure, the following equation can be written.

  $\Rightarrow x^{\circ }+{120}^{\circ }+{100}^{\circ }+{120}^{\circ }+{120}^{\circ }+{(x+10)}^{\circ }={720}^{\circ }$

  $\Rightarrow 2x^{\circ }+{470}^{\circ }={720}^{\circ }$

  $\Rightarrow 2x^{\circ }+{470}^{\circ }-{470}^{\circ }={720}^{\circ }-{470}^{\circ }$ (Subtracting ${470}^{\circ }$ on both sides)

  $\Rightarrow \frac{2x^{\circ }}{2}=\frac{{250}^{\circ }}{2}$ (Dividing both sides by $2$ )

  $\Rightarrow x^{\circ }={125}^{\circ }$

Conclusion:

Hence, the required value of x is ${125}^{\circ }.$