Question

In Fig. 4, find the measure of arc ADC, if angle OAB = 30° & angle OCB = 50°.

Answer 1

In triangle AOB,
Angle OAB = angle OBA ( angles between equal sides are equal)
=> OBA = 30°
So,
Angles OAB + OBA + BOA = 180°
=> 60° + BOA=180°
=>Angle BOA=120°

Similarly,
Angle BOC = 80°

Hence,
Measure of arc ADC = Angle AOC
= 360° - (120 + 80)°
= 160°

Answer 2

ATC In ΔAOB
∠OAB = ∠OBA ( angles between equal sides are equal)
=> ∠OBA = 30°
So,

∠OAB+∠OBA+∠BOA=180°
60°+ ∠ BOA = 180°
BOA = 120°
Similarly,
∠BOC = 80°
Hence
Measure of arc ADC = ∠AOC
= 360 - (120 + 80)
= 160