Round Mountain is closer to Hawthorne than Warm Springs is to Beatty.
Let's label the position of the towns with their initial and summarize the information given in the question.
Information
Consequence
The distance from Tonopah to Round Mountain is the same as the distance from Tonopah to Warm Springs.
TR≅TW
The distance from Tonopah to Hawthorne is the same as the distance from Tonopah to Beatty.
TH≅TB
We will indicate these congruences on the map. Let's also draw the segments HR and BW. We are asked to compare the length of these segments.
We can see that triangles △ HTR and △ BTW have two congruent sides. Since the included angle between the congruent sides is also given, the Hinge Theorem lets us compare the third sides of the triangles.
95>80 ⟹ m∠ BTW > m∠ HTR ⟹ BW>HR
Since BW is longer than HR, we can conclude that Round Mountain is closer to Hawthorne than Warm Springs is to Beatty.
