Answer:
The measure of ∠DBC is 72°.
Step-by-step explanation:
Given information: BD is a diameter, A is center of circle, Arc CB=36°.
According the angled inscribed in a semicircle theorem, the angle inscribed in a semicircle is a right angle.
[tex]\angle BCD=90^{\circ}[/tex]
According to the central angle theorem, the angle inscribed on the circle is half of its central angle.
[tex]\angle BDC=\frac{\angle BAC}{2}=\frac{36^{\circ}}{2}=18^{\circ}[/tex]
By angle sum property, the sum of interior angles of a triangle is 180 degrees.
[tex]\angle BDC+\angle BCD+\angle DBC=180[/tex]
[tex]18^{\circ}+90^{\circ}+\angle CBD=180^{\circ}[/tex]
[tex]108^{\circ}+\angle CBD=180^{\circ}[/tex]
[tex]\angle CBD=180^{\circ}-108^{\circ}[/tex]
[tex]\angle CBD=72^{\circ}[/tex]
Therefore the measure of ∠DBC is 72°.
