Chapter 7.4, Problem 16PSC

To determine

The set of possible values of angle V are to be calculated

Answer to Problem 16PSC

The set of possible values of angle V are $({36}^0,{60}^0,77{\frac{1}{7}}^0{90}^0,{100}^0,{108}^0)$

Explanation of Solution

Given information : The values of angle T are given as

  $105<m\angle T<145$

Based on the information that $105<m\angle T<145$ , we know that the possible values of T are in a

Pentagon, Hexagon, Heptagon, Octagon, Nonagon, and Decagon only

Thus, let us assume that the base angles of the triangle containing the angle T are x and y respectively. Thus, we get that the values of angle V can be

  $m\angle V={180}^0-2(x+y)$ , where

  $(x+y)={180}^0-m\angle T$

Thus, we substitute the value of x and y , and we get

  $m\angle V={180}^0-2({180}^0-m\angle T)=2m\angle T-{180}^0$

Now, we substitute the values of angle T to get the final values of angle V.

Thus, we get angle V equal to $({36}^0,{60}^0,77{\frac{1}{7}}^0{90}^0,{100}^0,{108}^0)$