Final answer:
The measure of vertical angles ∠A and ∠B are equal. So we set the given expressions for ∠A and ∠B equal to each other to solve for x. Substituting x = 7 into the expression for ∠B gives us 52 degrees as the measure of ∠B.
Step-by-step explanation:
The subject of this question is the concept of vertical angles in geometry. By definition, vertical angles are pairs of opposite angles made by two intersecting lines, and they are always congruent, which means they always have the same measure.
In this problem, ∠A and ∠B are vertical angles. Therefore, the measure of ∠A should equal the measure of ∠B, allowing us to set up the equation 8x - 4 = 7x + 3. Solving this equation will give us the value of x, which can then be substituted back into the expression for ∠B (7x + 3) to find the exact measure of angle B.
Solving the equation gets us: x = 7. Substituting x into the measure of ∠B, we get (7*7) + 3 = 52. So, the measure of ∠B is 52 degrees.
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