Chapter 15, Problem 10RP

To determine

To Find: The restrictions on the required angle of the given triangle.

Answer to Problem 10RP

  $60<x<150$

Explanation of Solution

Given:

  

Formula Used:

Angle-Inequality Theorem: It states that the exterior angle of any triangle is always greater than the both interior angle.

Calculation:

  $\begin{array}{l}x<{150}^0\left(\text{exterior angle inequality theorem}\right)\\ 180-x<120\left(\text{exterior angle inequality theorem}\right)\\ 180-120<x\\ 60<x\\ \text{ so by this the values of }x\text{ varies between 60 and 150}\\ 60<x<150\end{array}$

Conclusion:

  $\text{Thus by calcualting the values of }x,\text{ it varies between 60 and 150}$