Chapter 15.1, Problem 8PSB

To determine

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

Answer to Problem 8PSB

  $x<45$

Explanation of Solution

Given:

  $\angle X<\angle Y$

Formula Used:

  $a\left(c+d\right)=ac+ad$

Calculation:

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

Conclusion:

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