1 Answer

Sotti · Answer 1 · 2022-06-27T17:29:40+0000

Answer:

$\huge\purple {\boxed {m\angle FEG =23\degree}}$

$\huge \orange {\boxed {m\angle FEH=113\degree}}$

Explanation:

In the given circle,
$\overline{EG}$ is diameter and
$\overline{EH}$ is tangent at point E.

$\therefore \widehat {EFG}$ is a semicircular arc.

Since, measure of semicircular arc is 180°

$\therefore m(\widehat {EFG})=180\degree... (1)$

$\because m( \widehat {EF}) +m(\widehat {FG}) = m(\widehat {EFG})$ .... (2)

From equations (1) & (2)

$\therefore 134\degree +m(\widehat {FG}) = 180\degree$

$\therefore m(\widehat {FG}) = 180\degree-134\degree$

$\therefore m(\widehat {FG}) = 46\degree$

By inscribed angle theorem:

$m\angle FEG =(1)/(2) m(\widehat {FG} )$

$m\angle FEG =(1)/(2) * 46\degree$

$\huge\purple {\boxed {m\angle FEG =23\degree}}$

By tangent secant theorem:

$m\angle FEH=(1)/(2) (46\degree +180\degree)$

$m\angle FEH=(1)/(2) (226\degree)$

$\huge \orange {\boxed {m\angle FEH=113\degree}}$

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