Question

In the figure, if m(arc APC) = 60° and ZBAC = 80°, then find В. Q (i) Z ABC (ii) m(arc BQC) 80° , ​

Answer 1

Answer:

Given:

m( arc APC) = 60

angle BAC = 80

Find angle ABC and arc (BQC) =?

(a) For angle ABC

∠ ABC is the inscribed angle of arc APC

∴ By Inscribed angle theorem

m∠ ABC = ½ m(arc APC)

\begin{gathered}=\frac{}{2}\times60\\\end{gathered}

=

2

×60

m∠ ABC = 30°

(b) For arc (BQC)

Now, ∠ BAC is the inscribed angle of arc BQC,

∴ By Inscribed angle theorem,

m∠ BAC = ½ m(arc BQC)

80° = ½ m(arc BQC)

m(arc BQC) = 2 × 80°

m(arc BQC) = 160°

Hence m∠ ABC = 30° and m(arc BQC) = 160°