Question

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

Answer 1

Answer:

$\begin{gathered} x^{\circ}=70^{\circ} \\ y^{\circ}=55^{\circ} \\ z^{\circ}=55^{\circ} \end{gathered}$

Explanation:

Given that;

$AC=AB$

then triangle ABC is an isosceles triangle;

$\measuredangle C=\measuredangle B=\frac{180-\measuredangle A}{2}=\frac{180-70}{2}=55^{\circ}$

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;

$\begin{gathered} x^{\circ}=70^{\circ} \\ y^{\circ}=55^{\circ} \\ z^{\circ}=55^{\circ} \end{gathered}$