In the diagram, the value of $z$ is
(A) 150
(B) 180
(C) 60
(D) 90
(E) 120

![](https://cdn.mathpix.com/cropped/2024_04_20_46ead6524a8d61e21c51g-089.jpg?height=192&width=319&top_left_y=1796&top_left_x=1315)
In the diagram, the value of $z$ is
(A) 150
(B) 180
(C) 60
(D) 90
(E) 120

![](https://cdn.mathpix.com/cropped/2024_04_20_748fdafcde2a47412608g-386.jpg?height=230&width=385&top_left_y=633&top_left_x=1358)

## Solution

Since the angles of a triangle add to 180 ,

$$
\begin{aligned}
2 x r+3 x r+x r & =180 r \\
6 x r & =180 r \\
x & =30
\end{aligned}
$$

Now since the angles $x \mathrm{r}$ and $z \mathrm{r}$ together form a straight line, the

$$
\begin{aligned}
x \mathrm{r}+z \mathrm{r} & =180 \mathrm{r} \\
30 \mathrm{r}+z \mathrm{r} & =180 \mathrm{r} \\
z & =150
\end{aligned}
$$

ANSwER: (A)