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 = °

Question

07-07-2022
Mathematics

Answered

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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 = °

Sagot :

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swapnalimalwadeVT swapnalimalwadeVT · Answer 1 · 2022-07-09T02:02:48-04:00

The measures of GX = 13

The measures of [tex]\angle ABX=22^0[/tex]

EX = 4z + 1 and XF = 2z + 7

Take EX and XF equal time each other and then solve for z and then you will get GX because EX = XF = GX are congruent.

EX = XF

What is congruent?

Two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

4z + 1 = 2z + 7

2z = 6

z = 3

As, EX = XF = GX

EX = 4(3) + 1

EX = 13

Therefore, GX = 13 ------ ( EX = XF = GX )

To find the angle ABX, divide the angle ABC by 2 you will get

[tex]\angle ABX=22^0[/tex]

For more information, refer to the link given below

brainly.com/question/16548605

#SPJ1

Sagot :

What is congruent?

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