Chapter 9.6, Problem 30WE

To determine

To state: that measure of $\angle P$ .

Answer to Problem 30WE

It can be concluded that value of angle $P$ will be $\angle P>110°$

Explanation of Solution

Given Information:

  $\overline{PT}$ is a tangent. It os known that $80<marcRS<marcST<90$ .

Given figure,

  

Calculation:

Figure shows a circle with center $O$ , where $PT$ is a tangent to the circle.

And also consider that $80<marcRS<marcST<90$

Since measurement of $RS$ and $ST$ lies between 80 and 90,

Therefore, measurement of $RS+RT$ will be,

  $\begin{array}{c}mRS+mST<80+90\\ mRS+mST<170\end{array}$

Now measurement of complete circumference of circle is of $360°$ .

This means that,

  $\begin{array}{c}mRS+mST+mRT=360\\ mRS+170=360\end{array}$

Solve the above equation to get,

  $\begin{array}{c}mRS+170=360\\ mRS=360-170\\ =190\end{array}$

Therefore, $mRS>190$

As value of angle $P$ is $\angle P=mRT-mST$

Put the value in above equation to get,

  $\begin{array}{c}\angle P=mRT-mST\\ =190-80\\ =110\end{array}$

Therefore, it can be concluded that value of angle $P$ will be $\angle P>110°$