Final answer:
Given that ∠A and ∠B are vertical angles, their measures are equal. equating (2x+20)° and (3x+1)° and resolving, we find that x equals 19.
Step-by-step explanation:
The subject of this question is Mathematics, and it's based on the concept of vertical angles in geometry. According to the properties of vertical angles, these angles are always equal. So, if ∠A and ∠B are vertical angles, then their measures, m∠A and m∠B, would be equal.
So, (2x + 20)° = (3x + 1)°
Subtract 2x from both sides, we get:
20 = x + 1
Subtract 1 from both sides, we get:
x = 19.
So, the value of x that would make the measures of ∠A and ∠B equal is 19.
Learn more about vertical angles