Solve for x, y and z

I think x=60, y=30. Does z=90?

Thank you for your help.

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X=60 y=30 and z=90

I triangle ABC and triangle BCD.

AC=BC

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

x=y+30

=30+30

=60

Triangle BCD is an equilateral triangle.Therefore

30+60+z=180 (angle at one point A)

z=90

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.`

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