Question

= 110° and ZBAC 50°. Find ZDAC.
) = °
ABCD is a cyclic quadrilateral in which:
(1) BC-AD, ZADC
(ii) 2DBC = 80° and ZBAC = 40°. Find ZBCD.
i) ABCD = 100° and ZABD​

Answer 1

Answer:

ABCD is a cyclic quadrilateral.

Then, ∠ABC+∠ADC=180o ...[Opposite angles of a cyclic quadrilateral are supplementary]

⇒ ∠ABC=180∘−110∘=70∘.

In △ABC,

∠ABC+∠ACB+∠BAC=180o ...[Angle sum property]

⇒ 70o+∠ACB+50o=180o

⇒ ∠ACB=180∘−(50∘+70∘)=60∘.

Given, BC and AD are parallel.

⇒∠ACB=∠DAC=60∘ ...[Alternate interior angles].

Hence, option C is correct.

Answer 2

Abcd is a cyclic quadrilateral

then,

Angle a + angle b = 180°

50+ angle dac =180°

angle dac = 130.