Question

In the given figure A, B, C, D are Concyclic. If angle ACB =30 and angle BDC= 35
then find

(1) angle ADC
(2)angle ABC

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Answer 1

Sum of opposite angles of a cyclic quadrilateral = 180°

In cyclic quadrilateral ABCD:

⇒∠BAD + ∠ADC=180°

⇒50° + ∠ADC=180°

⇒∠ADC=180°

⇒ ∠ADC+∠CDE=180°

(Sum of angles on a straight line = 180°)

⇒ 130° + ∠CDE = 180°

⇒ ∠CDE = x = 50°

Answer 2

Answer:

Sum of opposite angles of a cyclic

quadrilateral = 180°

In cyclic quadrilateral ABCD:

→ <BAD + ZADC=180°

→ 50° + ZADC=180°

⇒ ZADC=180°

→ ZADC+2CDE=180°

(Sum of angles on a straight line = 180°)

→ 130° + LCDE = 180°

→ LCDE = x = 50°

Hope it helps you

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