Question

Given that mDE = 49° and mFG = 12°, find mFE.

Answer 1

119°

Step-by-step explanation:

`In\: \odot A,` GD is diameter.

`\therefore m\widehat{GFD} = 180\degree`

`\because m\widehat {FG} +m\widehat {DE} = m\widehat {FE} \widehat{GFD}`

`\therefore m\widehat {FG} +m\widehat {DE} + m\widehat {FE} = 180\degree`

`\therefore 49\degree +12\degree + m\widehat {FE} = 180\degree`

`\therefore 61\degree + m\widehat {FE} = 180\degree`

`\therefore m\widehat {FE} = 180\degree - 61\degree`

`\therefore m\widehat {FE} = 119\degree`

Answer 2

mFE = 119°

Step-by-step explanation:

mGB = 90°

mGB = mBD

∴ mGD = 180°

⇒ mFE = 180 - (mDE + mFG)

mFE = 180 - (49 + 12)

mFE = 180 - 61

mFE = 119°