Final answer:
The measure of angle AVB is equal to the sum of angles AFV and FVB. Without the value of the variable 'r', we cannot determine the exact measure of angle AVB, but we know it's 41 degrees plus twice the value of 'r'.
Step-by-step explanation:
The student's problem involves finding the measure of angle AVB given some algebraic expressions for angles in a geometric context. The question describes the relationship between multiple angles and includes algebraic expressions with a variable 'r'. From the information provided, we are given:
- ∑AVB = r - 4
- ∑AFV = 32
- ∑FVB = 2r + 9
To find ∑AVB, we can add ∑AFV and ∑FVB since angle AVB is the external angle for angle AFV and FVB and the external angle is equal to the sum of the opposite internal angles. Thus:
∑AVB = ∑AFV + ∑FVB
∑AVB = 32 + (2r + 9)
This means the measure of ∑AVB is 41 degrees plus twice the value of r.