Given:
• Measure of ∠ABC = 90 degrees
,
• Measure of ∠ABD = 8x + 1
,
• Measure of ∠DBC = 6x + 5
Let's find the measure of ∠DBC.
Since ∠ABC is a right angle, it measures 90 degrees.
Thus, we have:
m∠ABD + m∠DBC = 90
Now, we have the equation:

Let's solve for x in the equation:
Combine like terms.

Subtract 6 from both sides:

Divide both sides by 14:

Now, to find the measure of ∠DBC, substitute 6 for x in (6x + 5):
m∠DBC = 6(6) + 5
m∠DBC = 36 + 5
m∠DBC = 41 degrees.
• ANSWER:
41°