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

$a=\frac{1}{2}\times110^o$

$a=55^o$

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

$b=125^o$