Chapter 5.2, Problem 17PSA

To determine

To Find: A valid inequality and restriction on $x$ .

Answer to Problem 17PSA

  $\begin{array}{l}0°<30°<\left(3x-18\right)°\text{:Required inequality}\\ \therefore x>16\text{:Restriction on }x\end{array}$

Explanation of Solution

Given:

  

Concept Used:

Exterior angle is equal to the sum of two interior opposite angles.

Calculation:

Since, exterior angle is equal to the sum of two interior opposite angles.

  $\begin{array}{l}\angle ACD=\angle A+\angle B\\ \Rightarrow 0°<30°<\left(3x-18\right)°\\ \Rightarrow 0°<10°<\left(x-6\right)°\\ \Rightarrow 16<x\\ \therefore x>16\end{array}$