Final answer:
The theorem related to the measures of angles in the pair is the Angle Addition Postulate. To find the unknown angles, we use the Angle Addition Postulate and solve for x.
Step-by-step explanation:
The theorem related to the measures of angles in the pair is the Angle Addition Postulate.
According to the Angle Addition Postulate, the sum of two adjacent angles is equal to the measure of the larger angle formed by their union.
To find the unknown angle measures, we equate the sum of the given angles to the measure of the larger angle and solve for x:
(30x + 15)° + (50x - 65)° = measure of the larger angle
By simplifying and rearranging the equation, we can solve for x and find the values of the unknown angles.