T,V,S is an equilateral triangle (see below). The point V is such that the line segment from T to V is perpendicular to the line segment from R to S. CLASSIFY the inner triangle T,V,S by the measures of its angles and its sides.HINT:Since the line segment from T to S is opposite the right angle, it is the hypotenuse of the right triangle, T,V,S. Also, the angle between sides VS and ST is 60 degrees, because the triangle is equilateral.
APPLY: Set the sum of the measures of the angles of the triangle T,V,S to 180.
Then angle TSV + angle TVS + angle STV = 180.
Substituting "60" for angle TSV and "90" for angle TVS, we get
60 + 90 + angle STV = 180
150 + angle STV = 180
Therefore, angle STV=30.