Question

FC is the diameter of the circle. What is the measure of arc FAD?

Answer 1

`arc\ FAD=223^o`

Explanation:

we know that

The diameter divide a circle into two equal parts

so

The measure of arc FAC is equal to 180 degrees (Remember that a complete circle subtends a central angle of 360 degrees)

we have that

`arc\ AB=arc\ CD` ---> given problem

`arc\ AB=m\angle AGB` ----> by central angle

`m\angle AGB=43^o` ----> given problem

so

`arc\ AB=arc\ CD=43^o`

therefore

`arc\ FAD=arc\ FAC+arc\ CD` ----> by angle addition postulate

substitute

`arc\ FAD=180^o+43^o=223^o`