In figure, if m(arcAPC) = 600, ∠BAC = 800, find (a) ∠ABC (b) m(arcBQC)

Solution:

(a) ∠ ABC is the inscribed angle of arc APC

∴ By Inscribed angle theorem,

m∠ ABC = ½ m(arc APC)

∴m ∠ ABC = ½ [600] [Given]

∴ m∠ ABC = 300

(b) Now, ∠ BAC is the inscribed angle of arc BQC,

∴ By Inscribed angle theorem,

m∠ BAC = ½ m(arc BQC)

∴ 800 = ½ m(arc BQC)

∴ m(arc BQC) = 800 × 2

∴ m(arc BQC) = 1600

Ans. m∠ ABC = 300      and m(arc BQC) = 1600