Question

I need help on in the answer to the question

Answer 1

The given figure is

Recall that central angle =Intercepted arc .....(1)

`\text{Central angle=}\angle BOD=110^o`

`\text{Intercepted arc=BD}`

`\angle BOD=110^o=BD`

`BD=110^o`

Recall that inscribed angle=1/2 Intercepted arc ......(2)

`Inscribed\text{ angle =}\angle BAD=a`

`\text{Intercepted arc=BD=}110^o`

Substitute values in equation (2), we get

`a=(1)/(2)*110^o`

`a=55^o`

The quadrilateral ABCD inscribed in a circle is a cyclic quadrilateral.

The opposite angles in a cyclic quadrilateral are supplementary.

`\angle BAD=a=55^o\text{ and }\angle BCD=b\text{ are supplementary .}`

`a+b=180^0`

`\text{Substitute a=}55^o,\text{ we get}`

`55^o+b=180^o`

`b=180^o-55^o`

`b=125^o`

Hence the measure of b is

`b=125^o`