Question

Triangle W X Y is shown. All angles have different measures. Point S is equidistant from each side of the triangle. Lines are drawn from each point of the triangle to Point S. Congruent lines are also drawn from each side to the point to form right angles and form lines segments V S, T S, and U S. Angle S Y U is 39 degrees.
Given that point S is equidistant from the sides of ΔWXY, find the following measures.

SU =

mAngleSYW =
°

mAngleWXY =

Answer 1

SU = ST = SV (all three perpendicular segments from S to the sides are congruent — S is the incenter so they are all the inradius)

m∠SYW = 39° (SY is the bisector of ∠WYX, so the shown half-angle is 39°)

m∠WXY = 63°