Q:

Given: circle k(O), m FH = (31x+3°) m GH = (33x+3°) m∠FHG = (28x−3°) Find: m∠FGH

Accepted Solution

A:
Answer:The measure of angle FGH is m∠FGH=48°Step-by-step explanation:step 1Find the measure of arc FG in terms of xwe know thatThe inscribed angle measures half that of the arc comprisingm∠FHG=(1/2)[arc FG]substitute the given values (28x−3°)=(1/2)[arc FG] arc FG=(56x−6°)step 2Find the value of xwe know thatarc FG+arc FH+arc GH=360° -----> by complete circlesubstitute the values(56x−6°)+(31x+3°)+ (33x+3°)=360°120x=360°x=3°step 3Find the measure of angle m∠FGHwe know thatThe inscribed angle measures half that of the arc comprisingm∠FGH=(1/2)[arc FH]substitute the given valuesm∠FGH=(1/2)[31x+3°]m∠FGH=(1/2)[31(3)+3°]m∠FGH=48°