Question

AB is a diameter of a circle and ABCD is a
cyclic quadrilateral in that. If ACD = 40°,
then measurement of BAD ​

Answer 1

Answer:

140°

Step-by-step explanation:

A. B

D C

Is cyclic quadrilateral

then ,

measure of angle ACD + measure of angle BAD =180. ........( BY theorem of cyclic quadrilateral)

40°+BAD =180°

BAD =180°-40°

BAD =140°

Answer 2

The measurement of BAD=$50^{\circ}$

Step-by-step explanation:

Angle ACD=40 degrees

AB is a diameter of circle

Angle subtended by half circle at the circumference of  circle is equal to 90 degrees

Therefore, angle ACB=90 degree

Angle BCD=Angle ACB+angle ACD=40+90=130 degrees

We know that in cyclic quadrilateral

Sum of opposite angles of cyclic quadrilateral=180 degrees

By using this property

Angle BAD+angle BCD=180 degrees

Substitute the values

$130+\angle BAD=180$

$\angle BAD=180-130=50$

$\angle BAD=50^{\circ}$

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