Question

In the following figure, O is the centre of the circle. ∠ABC is inscribed in arc ABC and  ∠ ABC = 65°. Complete the following activity to find the measure of ∠AOC. 

∠ABC = `1/2`m ______  (Inscribed angle theorem) 
______ × 2 = m(arc AXC)  
m(arc AXC) = _______
∠AOC = m(arc AXC)  (Definition of measure of an arc)  
∠AOC = ______

Answer 1

∠ABC = `1/2`m Arc AXC (Inscribed angle theorem) 
65 × 2 = m(arc AXC)  
m(arc AXC) = 130°
∠AOC = m(arc AXC)  (Definition of measure of an arc)  
∠AOC = 130°