Question

#5
listen
find ( mangle abd ).
( mangle abd = square^circ )

Explanation:

Step1: Identify Angle Bisector

BD is the angle bisector? Wait, no, CD and AD are perpendicular to BC and BA respectively. So triangles BCD and BAD are right triangles. Also, since BD is common, and BC and BA? Wait, no, the angles: angle CBD is 20°, and since CD ⊥ BC and AD ⊥ BA, so BD is the angle bisector? Wait, no, the key is that the distance from D to BC and BA is equal? Wait, no, CD and AD are both perpendicular, so BD bisects angle ABC. Wait, angle CBD is 20°, so angle ABD should also be 20°? Wait, no, wait the diagram: CD is perpendicular to BC, AD is perpendicular to BA, so BD is the angle bisector, so angle ABD = angle CBD = 20°? Wait, no, maybe I misread. Wait, the angle at C is 20°, so angle CBD is 20°, and since AD and CD are both perpendicular, so triangles BCD and BAD are congruent? So angle ABD = angle CBD = 20°. So m∠ABD = 20.

Step2: Confirm with Angle Bisector Theorem

Since CD ⊥ BC and AD ⊥ BA, and D lies on BD, so BD is the angle bisector of ∠ABC. Thus, ∠ABD = ∠CBD = 20°.

Answer:

20