Final answer:
The measures of angles in a pair are related to the Angle Addition Postulate. By setting up an equation using the given angles, we can solve for the unknown angle measures. In this case, the unknown angle measures are 65 and 75.
Step-by-step explanation:
The measures of angles in a pair are related to the Angle Addition Postulate. According to this postulate, the measure of the whole angle is equal to the sum of the measures of its parts. In this case, we can set up an equation using the given angles:
m₂ = 10x + 15
m7 = 35x - 60
Since both angles are part of the same pair, their measures will add up to the measure of the whole angle. So we can set up the equation:
m₂ + m7 = 180
Substitute the given expressions for m₂ and m7 into the equation:
10x + 15 + 35x - 60 = 180
Combine like terms:
45x - 45 = 180
Now solve the equation for x:
45x = 225
x = 5
Substitute the value of x back into the expressions for m₂ and m7 to find the angle measures:
m₂ = 10(5) + 15 = 65
m7 = 35(5) - 60 = 75