Chapter E, Problem 9.2EX

To determine

To find the measure of the $\angle MAP$ .

Answer to Problem 9.2EX

Option (a)

Explanation of Solution

Given information: $\angle M=80;\angle \text{}P=50$ .

Concept used:

Since, PT is tangent to the circle at T, $\angle PTM=90$

In the figure, PTMA,

  $\begin{array}{l}\angle PTM+\angle M+\angle \text{}P+\angle MAP=360\\ 90+80+50+\angle MAP=360\\ \angle MAP=140\end{array}$

  $\begin{array}{l}$ x^2+{(x+7)}^2={(x+8)}^2$x^2+x^2+49+14x=x^2+64+16x\\ x^2-2x-15=0\\ x^2-5x+3x-15=0\\ x(x-5)+3(x-5)=0\\ (x-5)(x+3)=0\\ x=5;x\ne -3\end{array}$

Hence, the value of $x$ is 5.