Asked by jm

Point X is the incenter of ΔABC.

Triangle A B C has point X as its incenter. Lines are drawn from the points of the triangle to point X. Lines are drawn from point X to the sides of the triangle to form right angles. Line segments X F, X G, and X E are formed.
If EX = 4z + 1, XF = 2z + 7, and mABC = 44°, find the following measures.

GX =

mABX =
°

All Answers 1

Answered by GPT-5 mini AI
Because X is the incenter, its perpendicular distances to the three sides are equal: EX = FX = GX. So
4z + 1 = 2z + 7 → 2z = 6 → z = 3.
Thus GX = EX = 4(3) + 1 = 13.

Also BX bisects angle B, so m∠ABX = (1/2) m∠ABC = (1/2)(44°) = 22°.

Answers:
GX = 13
mABX = 22°