Question

12 find the m∠dbc. 5. (x + 9)° (11x - 3)°

Explanation:

Step1: Use the angle - bisector and right - angle relationship

Since \(BA\) bisects \(\angle ABD\), \(\angle ABD=(x + 9)^{\circ}\), and \(\angle DBC=(11x-3)^{\circ}\), and \(\angle ABC = 90^{\circ}\).
We know that \(\angle ABD+\angle DBC=90^{\circ}\).
Substitute the expressions: \((x + 9)+(11x-3)=90\).

Step2: Solve the equation for \(x\)

Combine like terms: \(x+11x+9 - 3=90\), which simplifies to \(12x+6 = 90\).
Subtract 6 from both sides: \(12x=90 - 6=84\).
Divide both sides by 12: \(x=\frac{84}{12}=7\).

Step3: Find the measure of \(\angle DBC\)

Substitute \(x = 7\) into the expression for \(\angle DBC\): \(\angle DBC=(11x-3)^{\circ}\).
\(\angle DBC=(11\times7 - 3)^{\circ}=(77-3)^{\circ}=74^{\circ}\).

Answer:

\(74^{\circ}\)