Question

use the figure and the given information to find the indicated measure. find ( mangle abc ) when ( ad = 3.2 ), ( cd = 3.2 ), and ( mangle dbc = 39^circ ).

Explanation:

Step1: Identify Angle Bisector

Since \(AD = CD = 3.2\) and \(\angle BAD=\angle BCD = 90^\circ\), \(BD\) is the perpendicular bisector of \(AC\), so \(BD\) bisects \(\angle ABC\).

Step2: Calculate \(\angle ABC\)

Given \(m\angle DBC = 39^\circ\), and \(BD\) bisects \(\angle ABC\), then \(m\angle ABC=2\times m\angle DBC\).

$$m\angle ABC = 2\times39^\circ = 78^\circ$$

Answer:

\(78\)