Question

HELPPP ASAP!! 10TH GRADE GEO

Answer 1

Answer:

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

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

Step-by-step 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:

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

$m\angle FEG =\frac{1}{2} \times 46\degree$

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

By tangent secant theorem:

$m\angle FEH=\frac{1}{2} (46\degree +180\degree)$

$m\angle FEH=\frac{1}{2} (226\degree)$

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