Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10: 9781285195698
ISBN 13: 978-1-28519-569-8

Chapter 2 - Section 2.4 - The Angles of a Triangle - Exercises - Page 93: 30


$\triangle$$RVS$ is a right $\triangle$

Work Step by Step

Because $\triangle$$RST$ is an equiangular triangle that means that all of the angles in the triangle are equal which means they must each be $60$$^{\circ}$. Since $\overline{RV}$ bisects $\angle$$SRT$ $\angle$$R$ must equal $30$$^{\circ}$ in $\triangle$$RVS$ and $\angle$$S$ equals $60$$^{\circ}$ since it is is part of an equilateral triangle. Now the sum of these two angles equals $90$$^{\circ}$ and we know that the sum of the interior angles of a triangle must equal $180$$^{\circ}$, we can prove that that $\angle$$V$ must equal $90$$^{\circ}$.
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