Question

is m∠1? 93° 131° m∠1 = °

Explanation:

Step1: Find the adjacent - interior angle to 131°

The adjacent - interior angle to the 131° exterior angle forms a linear pair. A linear pair of angles sums to 180°. Let the adjacent - interior angle be $x$. So, $x = 180^{\circ}-131^{\circ}=49^{\circ}$.

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. In the triangle, we know one angle is $x = 49^{\circ}$ and another is 93°. Let $\angle1$ be $y$. Then, $y+49^{\circ}+93^{\circ}=180^{\circ}$.
We can solve for $y$:
\[

$$\begin{align*} y&=180^{\circ}-(49^{\circ} + 93^{\circ})\\ y&=180^{\circ}-142^{\circ}\\ y& = 38^{\circ} \end{align*}$$

\]

Answer:

$38$