Final answer:
To find the measure of angle A, set the expressions for the measures of the vertical angles A and B equal, solve for x, and then substitute back into the expression for angle A. Solving the equation 4x + 14 = 5x - 5 gives x = 19. Substituting x into m∠A = (4x+14)° yields m∠A = 90°.
Step-by-step explanation:
The question involves finding the measure of ∠A when ∠A and ∠B are vertical angles with m∠A being (4x+14)° and m∠B being (5x-5)°.
Vertical angles are congruent, so their measures are equal.
Therefore, we set the expressions for the measures of angles A and B equal to each other to solve for x:
4x + 14 = 5x - 5
Add 5 to both sides:
4x + 19 = 5x
Subtract 4x from both sides:
19 = x
Inserting the value of x into the expression for m∠A:
m∠A = 4(19) + 14
m∠A = 76 + 14
m∠A = 90°.
The measure of ∠A is 90°.