Question

what is the value of n? a. 85° b. 47° c. 38° d. 81°

Explanation:

Step1: Find adjacent - interior angles

The angle adjacent to $133^{\circ}$ is $180 - 133=47^{\circ}$ (linear - pair of angles). The angle adjacent to $142^{\circ}$ is $180 - 142 = 38^{\circ}$ (linear - pair of angles).

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$. Let the three interior angles of the triangle be $47^{\circ}$, $38^{\circ}$, and $x$. Then $x=180-(47 + 38)=95^{\circ}$.
The angle $n$ and $x$ are a linear - pair. So $n = 180 - 95=85^{\circ}$.

Answer:

A. $85^{\circ}$