Question

1. In the figure. O is the centre of the
circle, angle BAC =80°, m(arc APC) = 60° then
find the measure of
(1) angle ABC (2) arc BQC.
​

Answer 1

Answer:

1. 40 degree.

80+60+BQc=180

140+BQC=180

BQC=180-140=40.

Its correct

Answer 2

(1) angle ABC = 30°

(2) arc BQC = 160°

The inscribed angle theorem states that, " The measure of an inscribed angle is half the measure of its intercepted arc.

So, we have, ∠ = 1/2 (m arc)

Given,

∠  BAC = 80°

m(arc APC) = 60°

(1) angle ABC

∠ = 1/2 (m arc)

∠ ABC = 1/2 (m arc APC)

= 1/2 × 60°

∴ ∠ ABC = 30°

(2) arc BQC

∠ = 1/2 (m arc)

∠ BAC = 1/2 (m arc BQC)

80° = 1/2 (m arc BQC)

2 × 80° = (m arc BQC)

∴ arc BQC = 160°