Final answer:
By setting up an equation based on the sum of angles EBD and DBC forming a straight line, we solve for x and find the measure of angle EBD to be 80 degrees.
Step-by-step explanation:
The problem appears to be about finding the measure of angle EBD (m∠EBD) when given two expressions for adjacent angles EBD and DBC, which together form a straight line. If m∠EBD is 4x + 16 and m_DBC is 6x + 4, we can use the fact that the sum of these two angles must be 180 degrees because they form a straight line (linear pair of angles).
To find the value of x, we set up the equation 4x + 16 + 6x + 4 = 180 and solve for x. Combining like terms, we get 10x + 20 = 180. Subtracting 20 from both sides gives us 10x = 160. Dividing both sides by 10, we find x = 16.
Now, we substitute x back into the expression for m∠EBD, which gives us 4(16) + 16 = 64 + 16 = 80 degrees. Therefore, the measure of angle EBD is 80 degrees, which corresponds to option (b).