Question

In the figure , (i) ZBAC = 70° and ZDAC 40°, then find BCD.
(ii) ZBAC = 60° and BCA = 20°, then find ZADC.
Plzz guys help me out

Answer 1

(ii) In ∆ ABC we have,

∠BAC + ∠BCA + ∠ABC = 180°

⇒ 60° + 20° + ∠ABC = 180°

∴ ∠ABC = 180° – 80° = 100°

∵ ABCD is an cyclic quatilateral,

∴ ∠ABC + ∠ADC = 180°

[∵ Opposite angles of a cyclic quatilateral are supplimentary]

⇒ 100° + ∠ADC = 180°

∴ ∠ADC = 180° – 100° = 80°

Answer 2

Step-by-step explanation:

In ΔABC, we have

∠BAC+∠BCA+∠ABC=180

∘

....[Angle sum property]

⇒60

∘

+20

∘

+∠ABC=180

o

∴∠ABC=180

∘

−80

∘

=100

∘

.

ABCD is a cyclic quadrilateral,

∴∠ABC+∠ADC=180

∘

.....[Since, opposite angles of a cyclic quadrilateral are supplementary]

⟹ 100

∘

+∠ADC=180

∘

⟹∠ADC=180

∘

−100

∘

=80

Hope it helps you!

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