Q. 34.5( 13 Votes )

# In ΔABC, AC=BC and BC is extended upto the point D. If ∠ACD=144°, then let us determine the circular value of each of the angles of ΔABC.

Answer :

∠ACD = 144°

∵ DCB is straight line, ∠DCB = 180°

⇒ ∠ACB = 180° - 144° = 36°

∵ AC=BC, by opposite angle property

⇒ ∠CAB = ∠CBA = x

By Angle sum Property

⇒ ∠CAB + ∠CBA + ∠ACB = 180°

⇒ 2x + 36° = 180°

⇒ x = 72°

⇒ ∠CAB = ∠CBA = 72° and ∠ACB = 36°

And ∠ACB = 36°

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