Question

bd bisects ∠abc. solve for x and find m∠abc. m∠abd = (7x)°, m∠dbc = (2x + 15)° x = \boxed{}

Explanation:

Step1: Use angle bisector definition

Since \( \overrightarrow{BD} \) bisects \( \angle ABC \), \( m\angle ABD = m\angle DBC \). So we set \( 7x = 2x + 15 \).

Step2: Solve for x

Subtract \( 2x \) from both sides: \( 7x - 2x = 15 \), which simplifies to \( 5x = 15 \). Then divide both sides by 5: \( x = \frac{15}{5} = 3 \).

Answer:

\( x = 3 \)