Question

what is the value of p? p = \boxed{^\circ}

Explanation:

Step1: Use triangle angle sum property

In a triangle, the sum of interior angles is $180^\circ$. Also, the angle adjacent to $p$ and $z + 41^\circ$ is supplementary, so the third angle of the triangle (the right - angled part? Wait, no, the triangle has angles $z-18^\circ$, $z$, and the angle adjacent to $p$. Wait, actually, the angle adjacent to $p$ and $z + 41^\circ$ form a linear pair, so the angle inside the triangle at that vertex is $180^\circ-(z + 41^\circ)$. Then, by triangle angle sum: $(z-18^\circ)+z+(180^\circ-(z + 41^\circ))=180^\circ$.

Simplify the left - hand side:
\[

$$\begin{align*} z-18+z + 180 - z-41&=180\\ z+( - 18+180 - 41)&=180\\ z + 121&=180\\ z&=180 - 121\\ z&=59 \end{align*}$$

\]

Step2: Find $p$ using linear pair

Since $p$ and $z + 41^\circ$ form a linear pair, $p+(z + 41^\circ)=180^\circ$. We know $z = 59^\circ$, so substitute $z$:

\[

$$\begin{align*} p+(59 + 41)&=180\\ p + 100&=180\\ p&=180 - 100\\ p&=80 \end{align*}$$

\]

Answer:

$80$