Question

Use the diagram to find the measure of arc. AB and CD and the diameters of the circle F

Answer 1

11).
`m(\widehat{DE})` = 90°

12).
`m(\widehat{AEC})` = 212°

Explanation:

A circle F with AB and CD are the diameters has been given in the figure attached.

11). Since,
`m(\widehat{AB})` = 180°

and
`m(\widehat{AB})=m(\widehat{AD})+m(\widehat{DE})+m(\widehat{BE})`

Therefore,
`m(\widehat{AD})+m(\widehat{DE})+m(\widehat{BE})` = 180°

32° +
`m(\widehat{DE})` + 58° = 180°

`m(\widehat{DE})` = 180° - 90°

= 90°

12. Since,
`m(\widehat{AD})=m(\widehat{BC})` = 32°

`m(\widehat{AEC})` =
`m(\widehat{AB})+m(\widehat{BC})`

= 180° + 32°

= 212°