Chapter 15.1, Problem 7PSB

To determine

To Find: The restrictions on the measure of the original angle.

Answer to Problem 7PSB

  $x>45$

Explanation of Solution

Given:

  $\begin{array}{l}x\text{ is the given angle;}\\ \left(90-x\right)\text{ is the complement}\end{array}$

Formula Used:

  $a\left(c+d\right)=ac+ad$

Calculation:

  $\begin{array}{l}x\text{ is the given angle;}\\ \left(90-x\right)\text{ is the complement}\\ \text{⇒}x>90-x\\ \text{⇒}x+x>90\\ \text{⇒}2x>90\\ \text{⇒}x>\frac{90}{2}\\ \text{⇒}x>45\end{array}$

Conclusion:

Thus, the required restrictions is $x>45$ .