Final answer:
To find the measure of ∠A, we solve the equation formed by the two supplementary angles, which gives us x = 16°. When we substitute x back into the expression for ∠A, we get ∠A = 48°. Correct option is (A) 8x − 4°.
Step-by-step explanation:
The question involves finding the measure of ∠A when angles A and B are supplementary and their measures are given by m_A = (4x − 16)° and m_B = (8x + 4)°. Since they are supplementary, their measures add up to 180°, so we can set up the equation (4x − 16) + (8x + 4) = 180. Solving this equation will give us the value of x, and then we can find m_A by substituting x back into the expression for m_A.
First, let's add the expressions for m_A and m_B:
(4x − 16) + (8x + 4) = 180°
Combine like terms:
12x − 12 = 180°
Add 12 to both sides:
12x = 192°
Divide by 12:
x = 16°
Now, substitute x back into m_A:
m_A = (4x − 16)°
m_A = (4(16) − 16)°
m_A = (64 − 16)°
m_A = 48°
Thus, the measure of ∠A is 48°, which corresponds to option (A) 8x − 4°.