Chapter 4.6, Problem 48HP

To determine

To explain:

The correct statement from Alexis and Miguela for the given information.

Answer to Problem 48HP

Neither of them is correct.

Explanation of Solution

Given Information:

Alexis and Miguela arefinding $m\angle G$ in the figure shown. Alexis says that $m\angle G=35$ , while Miguela says that $m\angle G=60$ .

  

Neither of them is correct.

This is an isoscelestriangle with a vertex angle of $70$ . Since this is anisosceles triangle, the base angles are congruent.

  $\begin{array}{l}m\angle F+m\angle G+m\angle H=180\\ 70+m\angle G+m\angle H=180\\ m\angle G+m\angle H=110\mathrm{...}Subtract-70frombothsides.\\ m\angle G+m\angle G=110\mathrm{...}Substitutethevalue\\ 2m\angle G=110\\ m\angle G=\frac{110}{2}\\ m\angle G=55\end{array}$

Thus, the correct value of $m\angle G=55$ .