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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 = °

Answer :

The value of GX is 13 and m ∠ABX is 22°

How to determine the angles

With the information, we have

EX = 4z + 1  and XF = 2z + 7

It is important to note that  EX = XF = GX are congruent, that is, they are equal

Equate EX = XF to determine z

4z + 1 = 2z + 7

Collect like terms

2z = 6

z = 3

We know that  EX = XF = GX and x = 3, substitute into the value of any one

EX = 4(3) + 1

EX = 13

EX = GX

GX = 13

To determine m ∠ABX, we divide m ∠ABC by 2

We have

m ∠ABX  = 44/2

m ∠ABX = 22°

Therefore, the value of GX is 13 and m ∠ABX is 22°

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