Question

1. find ( mangle abd ).

( mangle abd=square^{circ} )
geometry: fl 2023>chapter 6>section 6.2: bisectors of triangles>6.2: review & refresh (49 - 60)>question #55

Explanation:

Step1: Recall the Angle Bisector Theorem

If a point is on the bisector of an angle, then it is equidistant from the sides of the angle. Here, \(DA = DC\) (marked as equal), so \(BD\) is the angle bisector of \(\angle ABC\).

Step2: Calculate \(m\angle ABD\)

Since \(BD\) bisects \(\angle ABC\) and \(m\angle ABC=30^{\circ}\), then \(m\angle ABD=\frac{1}{2}m\angle ABC\).
Substitute \(m\angle ABC = 30^{\circ}\) into the formula: \(m\angle ABD=\frac{1}{2}\times30^{\circ}\)

Answer:

\(15\)