Question

How do I write down the size of each angles mark by letters for this question?

Answer 1

Ok, so

We want to write the size of each angles:

Remember that 105° and z are supplementary angles. So, we can write:

`\begin{gathered} 105+z=180 \\ z=180-105 \\ z=75 \end{gathered}`

Notice that both lines are parallel. So,

`\angle x=\angle z=75`

Now, as you can see, the vertical lines and the horizontal lines are parallel, then, we can say that the figure is a parallelogram.

For this reason, remember that, in a parallelogram:

Two pairs of angles are the same, and the sum of all internal angles in a parallelogram is always 360°.

Therefore,

`\begin{gathered} 105+105+2y=360 \\ 210+2y=360 \\ 2y=150 \\ y=75 \end{gathered}`

Then,

`\begin{gathered} \angle x=75 \\ \angle y=75 \\ \angle z=75 \end{gathered}`