Given: circle k(o), m fh = (31x+3°) m gh = (33x+3°) m∠fhg = (28x−3°) find: m∠fgh

The measure of angle FGH is m∠FGH=48°

Step-by-step explanation:

step 1

Find the measure of arc FG in terms of x

we know that

The inscribed angle measures half that of the arc comprising

m∠FHG=(1/2)[arc FG]

substitute the given values

(28x−3°)=(1/2)[arc FG]

arc FG=(56x−6°)

step 2

Find the value of x

we know that

arc FG+arc FH+arc GH=360° > by complete circle

substitute the values

(56x−6°)+(31x+3°)+ (33x+3°)=360°

120x=360°

x=3°

step 3

Find the measure of angle m∠FGH

we know that

The inscribed angle measures half that of the arc comprising

m∠FGH=(1/2)[arc FH]

substitute the given values

m∠FGH=(1/2)[31x+3°]

m∠FGH=(1/2)[31(3)+3°]

m∠FGH=48°