Answer
a) x=11
$m\angle FGH=30$
b) $m\angle HGI=30$
c) $m\angle FGI=60$
Work Step by Step
a) Use the definition of a bisector:
$3x-3=4x-14$
Subtract 3x from each side.
$3x-3-3x=4x-14-3x$
$-3=x-14$
Add 14 to each side.
$-3+14=x-14+14$
$11=x$
Substitute to find the measure.
$m\angle FGH=3x-3=3(11)-3=33-3=30$
b) Substitute to find the measure.
$m\angle HGI=4x-14=4(11)-14=44-14=30$
c) Use the definition of a bisector:
$m\angle FGI=m\angle FGH+m\angle HGI=30+30=60$
