Question

what is m∠1?
m∠1 = \underline{\quad\quad} °

Explanation:

Step1: Find the interior angle adjacent to ∠1

First, calculate the unknown interior angle of the triangle using the angle sum property of triangles (sum of interior angles = $180^\circ$).
Let the unknown interior angle be $x$.
$x + 42^\circ + 78^\circ = 180^\circ$
$x = 180^\circ - 42^\circ - 78^\circ = 60^\circ$

Step2: Calculate m∠1 using linear pair

∠1 and $x$ form a linear pair (sum to $180^\circ$).
$m\angle1 + x = 180^\circ$
$m\angle1 = 180^\circ - 60^\circ$

Answer:

$120^\circ$