Can someone help me solve for this side?

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1 Answer
Sean
Apr 24, 2018

#XZ=55#

Explanation:

.

Angle #/_YXZ# is facing arc #YZ#.

Angle #/_XYZ# is facing arc #XZ#.

Arc #YZ# and arc #XZ# are equal to each other. Therefore,

#/_YXZ = /_XYZ#

This means that triangle #DeltaXYZ# is an isoceles triangle with sides #XZ# and #YZ# equal to each other. As such, we can put their measures equal to each other and solve for #x#:

#6x+10=8x-5#

#2x=15#

#x=15/2#

Now, we can plug this value in for #x# in the measure of #XZ#:

#XZ=6x+10=6(15/2)+10=45+10=55#

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