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 =
✔ 39
°

mAngleWXY =
°

Answer 1

SU = ST = SV (S is the incenter so the perpendiculars to the three sides are congruent)

m∠SYW = 39° (given / SY bisects ∠Y)

m∠WXY = 51°

Reason (brief): S is the incenter, so SY bisects ∠Y; hence ∠Y = 2·39° = 78°. Also SU ⟂ WY, so ∠YSU = 90° − 39° = 51°, which gives ∠WXY = 51°.