# Side AB of a cyclic Quadrilateral ABCD is extended upto X. If ∠XBC = 105° then ∠ADC ?

## Answers

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0

**Answer:**

**Step-by-step explanation:**

ABCD is a cyclic quadrilateral with AB as the diameter of the circle.

Also, ∠ADC=140

o

.

We have to find: ∠BAC.

Then,

∠ADC+∠ABC=180

o

....(since the sum of the opposite angles of a quadrilateral is 180

o

).

∴∠ABC=180

o

−140

o

=40

o

.

Also, ∠ACB=90

o

....(since the angle subtended by a diameter at the circumference of the circle, is 90

o

).

∴ In ΔABC we have,

∠ACB=90

o

and ∠ABC=40

o

.

So, ∠CAB=180

o

−(∠ACB+∠ABC)

=180

o

−(90

o

+40

o

)

∴∠BAC=50

o

.

Hence, option B is correct.

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