Final answer:
To find the measure of ∠A, set the expressions for vertical angles ∠A and ∠B equal to each other and solve for x. After calculating, the value of x is 32, which gives us the measure of ∠A as 115°.
Step-by-step explanation:
To solve the mathematical problem completely, we need to use the property that vertical angles are equal. Since ∠A and ∠B are vertical angles, their measures are equal. Thus, we can set the expressions for their measures equal to each other and solve for x:
m∠A = (4x - 13)°
m∠B = (3x + 19)°
Since m∠A = m∠B, we have:
4x - 13 = 3x + 19
Now, we will solve for x:
Subtract 3x from both sides: 4x - 3x - 13 = 3x - 3x + 19, which simplifies to x - 13 = 19.
Add 13 to both sides: x - 13 + 13 = 19 + 13, so x = 32.
Now that we have the value of x, we can find the measure of ∠A:
m∠A = 4x - 13 = 4(32) - 13 = 128 - 13 = 115°
Therefore, the measure of ∠A is 115°.