Chapter 8.2, Problem 18PSC

To determine

To find:The value of $m\angle F$ .

Answer to Problem 18PSC

The value of angle is 33 $°$

Explanation of Solution

Given information Two given triangles are similar, i.e., $\Delta ABC\sim \Delta DEF$

  $\begin{array}{l}m\angle A=50,m\angle D=2x+5y\\ m\angle F=5x+y,m\angle B=102-x\end{array}$

Formula used In similar triangles, corresponding angles are equal

Calculation In given similar triangles, we have $$

  $\begin{array}{l}In\Delta ABC,\\ \angle A+\angle B+\angle C=180°\\ \Rightarrow 50°+102-x+\angle C=180°\\ \Rightarrow \angle C=28+x\mathrm{........}\left(i\right)\\ \angle A=\angle D\\ \Rightarrow 2x+5y=\mathrm{50.........}\left(ii\right)\\ \angle C=\angle F\\ \Rightarrow 28+x=5x+y\\ \Rightarrow 4x+y=\mathrm{28.........}\left(iii\right)\end{array}$

  $\begin{array}{l}\left(iii\right)\times 5-\left(ii\right),\\ 18x=90\\ \Rightarrow x=5\\ \Rightarrow \angle C=28+5=33°\\ \therefore \angle F=\angle C=33°\end{array}$