Chapter 3.4, Problem 22WE

To determine

The value of $m\angle T$

Answer to Problem 22WE

Value of angle $m\angle T<{70}^0$

Explanation of Solution

Given :

  $m\angle R={90}^0\text{ and }m\angle S>{20}^0$

According to property of triangle sum of angles of a triangle is ${180}^0$

Therefore,

  $m\angle R+m\angle S+m\angle T={180}^0$

For, $m\angle S>{20}^0$

  $\begin{array}{l}m\angle R+m\angle S+m\angle T<{180}^0\\ {90}^0+{20}^0+m\angle T<{180}^0\\ {110}^0+m\angle T<{180}^0\\ m\angle T<{70}^0\end{array}$

Therefore, angle $m\angle T<{70}^0$