Question

what is the value of the unknown angle measure? enter the answer.

Explanation:

Step1: Find interior adjacent angle

The exterior angle and its adjacent interior angle are supplementary (sum to $180^\circ$).
$180^\circ - 142^\circ = 38^\circ$

Step2: Calculate unknown interior angle

Sum of triangle interior angles is $180^\circ$. Subtract the two known angles.
$180^\circ - 75^\circ - 38^\circ = 67^\circ$

Answer:

$67$