Question

what is ( mangle cbd )?( mangle cbd=)

Explanation:

Step1: Find the measure of ∠ADB

Since the sum of angles in a triangle is \(180^{\circ}\), in \(\triangle ABD\), \(\angle A = 60^{\circ}\), \(\angle ABD=80^{\circ}\). Then \(\angle ADB=180^{\circ}-(60^{\circ} + 80^{\circ})=40^{\circ}\).

Step2: Use the exterior - angle property

\(\angle ADB\) is an exterior angle of \(\triangle BCD\). By the exterior - angle property of a triangle (\(\angle ADB=\angle CBD+\angle C\)), and we know \(\angle ADB = 40^{\circ}\), \(\angle C = 35^{\circ}\).
So \(\angle CBD=\angle ADB-\angle C\).
Substitute the values: \(\angle CBD=40^{\circ}-35^{\circ}\).

Answer:

\(5^{\circ}\)