Question

3. find X, Y, and ZShow exact steps used to solve

Answer 1

`\begin{gathered} x^(\circ)=70^(\circ) \\ y^(\circ)=55^(\circ) \\ z^(\circ)=55^(\circ) \end{gathered}`

Step-by-step explanation:

Given that;

`AC=AB`

then triangle ABC is an isosceles triangle;

`\measuredangle C=\measuredangle B=(180-\measuredangle A)/(2)=(180-70)/(2)=55^(\circ)`

From the given figure, we can observe that quadrilateral ADFE is a parallelogram.

Recall that opposite angles of a parallelogram are equal.

So, we have;

`\begin{gathered} x^(\circ)=\measuredangle A \\ x^(\circ)=70^(\circ) \end{gathered}`

Also, the same rule applies to parallelogram BFDE and CDEF;

So, we have;

`\begin{gathered} y^(\circ)=\measuredangle B=55^(\circ) \\ y^(\circ)=55^(\circ) \end{gathered}`
`\begin{gathered} z^(\circ)=\measuredangle C=55^(\circ) \\ z^(\circ)=55^(\circ) \end{gathered}`

Therefore, we have;

`\begin{gathered} x^(\circ)=70^(\circ) \\ y^(\circ)=55^(\circ) \\ z^(\circ)=55^(\circ) \end{gathered}`