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°

11 feet 6 inches and 8 feet 6 inches

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.