Question

3 as shown in the figure below, a, b and c are on ⊙o. if m∠cbo = 40°, then m∠a is ____. 4 as shown in the figure, a, b, and c are on ⊙o, and m∠oab = 55°. then m∠acb = ____ °.

Explanation:

Step1: Recall circle - property for question 3

In $\odot O$, $OB = OC$ (radii of the same circle). So $\angle OCB=\angle CBO = 40^{\circ}$. The central - angle $\angle BOC=180^{\circ}-2\times40^{\circ}=100^{\circ}$. The inscribed - angle $\angle A=\frac{1}{2}\angle BOC$. So $\angle A = 40^{\circ}$.

Step2: Recall circle - property for question 4

In $\odot O$, $OA = OB$ (radii of the same circle). So $\angle OBA=\angle OAB = 55^{\circ}$. Then $\angle AOB=180^{\circ}-2\times55^{\circ}=70^{\circ}$. The inscribed - angle $\angle ACB=\frac{1}{2}\angle AOB$. So $\angle ACB = 35^{\circ}$.

Answer:

1. $40^{\circ}$
2. $35^{\circ}$