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In order to find the measures of angles x, y, and z we will need to understand some conjectures about triangles.
First, in an isosceles triangle (a triangle with 2 = sides), the base angles (the angles opposite the 2 = sides) are also equal. So this means that `y = 30.`
Also, in an equilateral triangle (triangle with all sides equal) all angles are equal to each other. Since all 3 angles in a triangle must be equal to 180. Each angle in the equilateral triangle must equal 60. So, `x = 60.`
Now, the three angles consisting with z must all add to 180 because all three together form a straight angle which equals 180.
Therefore, y + (top angle of equilateral, which =60) + z = 180
So, 30 + 60 + z = 180. Solve for z and z = 90.
Answers make: `x = 60, y = 30, and z = 90.`
X=60 y=30 and z=90
I triangle ABC and triangle BCD.
triangle ABC is an isosceles triangle,
the angle pposite to equal sides are equal.
There fore y=30.
x is an exterior angle of triangle ABC
Triangle BCD is an equilateral triangle.Therefore
30+60+z=180 (angle at one point A)
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