Question

solve for ( mangle dbc ) if ( mangle abc = 130^{circ} ) and ( mangle abd = 90^{circ} ).

Explanation:

Step1: Analyze the relationship between angles

We know that \(m\angle ABC=m\angle ABD + m\angle DBC\) (angle - addition postulate).

Step2: Solve for \(m\angle DBC\)

Rearrange the formula: \(m\angle DBC=m\angle ABC - m\angle ABD\).
Substitute \(m\angle ABC = 130^{\circ}\) and \(m\angle ABD=90^{\circ}\) into the formula: \(m\angle DBC = 130^{\circ}-90^{\circ}\).

Answer:

\(40^{\circ}\)