Question

ray bc bisects ∠abd. if m∠abd = 78°, what is m∠cbd in degrees? enter the correct answer in the box.

Explanation:

Step1: Recall the definition of an angle bisector

An angle bisector divides an angle into two equal - measure angles. So, if ray \(BC\) bisects \(\angle ABD\), then \(\angle ABC=\angle CBD\) and \(m\angle ABD = m\angle ABC + m\angle CBD=2m\angle CBD\).

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

We know that \(m\angle ABD = 78^{\circ}\) and \(m\angle ABD = 2m\angle CBD\). So we can set up the equation \(2m\angle CBD=78^{\circ}\). To find \(m\angle CBD\), we divide both sides of the equation by 2: \(m\angle CBD=\frac{78^{\circ}}{2}\)

Step3: Calculate the value

\(\frac{78^{\circ}}{2} = 39^{\circ}\)

Answer:

\(39\)