Chapter 15.1, Problem 10PSB

To determine

To Find: The restrictions on the measure of the angle and the complement.

Answer to Problem 10PSB

  $x>60$

Explanation of Solution

Given:

  $\text{An angle is greater than twice its compliment}\text{.}$

Formula Used:

  $a\left(c+d\right)=ac+ad$

Calculation:

  $\begin{array}{l}x\text{ is the given angle;}\\ \left(90-x\right)\text{ is the complement}\\ \text{⇒}x>2\left(90-x\right)\\ \text{⇒}x>180-2x\\ \text{⇒}x+2x>180\\ \text{⇒}3x>180\\ \text{⇒}x>60\end{array}$

Conclusion:

Thus, the required restrictions is $x>60$ .