Question

in the figure below, △nop is drawn. the line qr is drawn such that qr||op. m∠nop =
<
because they are

Explanation:

Step1: Use property of parallel lines

When $QR\parallel OP$, corresponding - angles are equal. So, the angle corresponding to the $45^{\circ}$ angle formed by $QR$ and $NO$ is also $45^{\circ}$.

Step2: Apply angle - sum property of a triangle

In $\triangle NOP$, we know that the sum of interior angles of a triangle is $180^{\circ}$. Let $\angle NOP = x$. Given one angle is $45^{\circ}$ and another is $50^{\circ}$. Then $x+45^{\circ}+50^{\circ}=180^{\circ}$.
We can solve for $x$ as follows:
\[

$$\begin{align*} x&=180^{\circ}-(45^{\circ} + 50^{\circ})\\ x&=180^{\circ}-95^{\circ}\\ x& = 85^{\circ} \end{align*}$$

\]

Answer:

$85^{\circ}$