Question

solve for ( mangle abc ) if ( mangle abd = 72^{circ} ) and ( mangle dbc = 75^{circ} ).

Explanation:

Step1: Use angle - addition postulate

By the angle - addition postulate, \(m\angle ABC=m\angle ABD + m\angle DBC\).

Step2: Substitute the given values

We know that \(m\angle ABD = 72^{\circ}\) and \(m\angle DBC=75^{\circ}\). Substitute these values into the formula: \(m\angle ABC=72^{\circ}+75^{\circ}\).

Step3: Calculate the sum

\(72 + 75=147\), so \(m\angle ABC = 147^{\circ}\).

Answer:

\(147\)