Chapter 15.2, Problem 1PSA

To determine

To Find: The restrictions on the required angle.

Answer to Problem 1PSA

  $\begin{array}{l}\text{So the contraction of }\angle \text{1 stands between }\\ 80<\angle 1<{180}^0.\end{array}$

Explanation of Solution

Given:

  ${\text{Interior angle 80}}^o.$

  

Formula Used:

Exterior Angle Theorem: It states that exterior angle is sum of two interior angle.

Calculation:

  $\begin{array}{l}{\text{ since the interior angle is 80}}^0{\text{ and the other angle needs to be atleast 1}}^0.\\ \text{the exterior angle theorem states that }\angle \text{1 has to be equivalent to the sum of the two remote interior angles}\text{.}\\ \text{so by this}\\ \angle 1>{81}^0\\ {\text{and it should be less than 180}}^{0.}so,\\ \angle 1<{180}^0\\ \text{So the contraction of }\angle \text{1 stands between }\\ 80<\angle 1<{180}^0.\end{array}$

Conclusion:

Thus, $\angle 1{\text{ stands less than 180}}^0{\text{ and more than 80}}^0.$