Question

what is $m\angle 1$?
(there is a triangle with angles 35° and 67°, and angle 1 is adjacent to the triangle on a vertical line. $m\angle 1 = \square ^\circ$)

Explanation:

Step1: Find triangle's third interior angle

First, calculate the unknown interior angle of the triangle using the fact that the sum of interior angles in a triangle is $180^\circ$.
Let the unknown interior angle be $x$.
$x = 180^\circ - 67^\circ - 35^\circ = 78^\circ$

Step2: Relate to $\angle 1$ (supplementary angles)

$\angle 1$ and $x$ are supplementary (they form a straight line, sum to $180^\circ$).
$m\angle 1 = 180^\circ - 78^\circ$

Answer:

$102^\circ$