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sergejj [24]
3 years ago
13

Find the lengths of BC and XZ and the measure of BZX

Mathematics
1 answer:
Ann [662]3 years ago
4 0
BC = 12; XZ = 8; BZX = 55

To find BC:
Since XY is the bisector of AB and AC, this means that it is a median of triangle ABC.  Its length will be half of the length of BC; 6 = 1/2BC; 6*2 = BC; 12 = BC

To find XZ:
Since XZ is the bisector of AB and BC, this means that it is a median of triangle ABC.  Its length will be half of the length of AC; 1/2(16) = 8.

To find BZX:

XYCZ is a parallelogram.  Consecutive angles of a parallelogram are supplementary; 180-55=125=XZC.

XZC and BZX form a linear pair and are thus supplementary.  This means that BZX = 180-XZC = 180-125 = 55
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(

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(

2

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2

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(

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(

−

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x

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2

(

2

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6

)

=

12

x

(

3

)

(

4

x

2

)

=

12

x

2

(

3

)

(

−

5

x

)

=

−

15

x

(

3

)

(

6

)

=

18

And now we add them all up (I'm going to group terms in the adding):

8

x

3

−

10

x

2

+

12

x

2

+

12

x

−

15

x

+

18

And now simplify:

8

x

3

+

2

x

2

−

3

x

+

18

Step-by-step explanation:

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Answer:

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