SOLUTION: This is a worksheet and we have no book so will you please help. In triangle XYZ, XY=~YZ. If m angleX=52, find m angle Y. We have to show our work. Thanks

Algebra ->  Triangles -> SOLUTION: This is a worksheet and we have no book so will you please help. In triangle XYZ, XY=~YZ. If m angleX=52, find m angle Y. We have to show our work. Thanks      Log On


   

Question 161599: This is a worksheet and we have no book so will you please help.
In triangle XYZ, XY=~YZ. If m angleX=52, find m angle Y. We have to show our work.
Thanks
Answer by gonzo(654) About Me  (Show Source):
You can put this solution on YOUR website!
triangle xyz
xy = yz
angle x = 52 degrees.
draw triangle with x on the left, y on top, z on the right.
xy is line going up from left to right.
yz is line going down from left to right.
angle x is the angle in the left hand corner of the triangle.
this is an isosceles triangle because 2 sides are equal (congruent).
in an isosceles triangle the base angles are equal.
these are the angles opposite the equal sides.
angle x is opposite yz
angle z is opposite xy
angle z is therefore equal to angle x is equal to 52 degrees.
since the sum of the interior angles of a triangle is always 180, then angle y must be equal to 180 - angle x - angle z.
this becomes angle y = 180 - 2*52 = 180 - 104 = 76.
angle y must be 76 degrees.
to prove add all 3 angles of the triangle and they must equal 180 degrees.
52 + 52 + 76 = 180.
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angle y is 76 degrees.