Question

In the diagram of circle R, m∠FGH is 50°. What is m? 130° 230° 260° 310°

Answer 1

we know that

The measurement of the exterior angle is the semi-difference of the arcs which comprises

In this problem

∠FGH is the exterior angle

∠FGH=
`50\°`

∠FGH=
`(1)/(2)(arc\ FEH-arc\ FH)`

`50\°=(1)/(2)(arc\ FEH-arc\ FH)`

`100\°=(arc\ FEH-arc\ FH)` -----> equation A

`arc\ FEH+arc\ FH=360\°`

`arc\ FH=360\°-arc\ FEH` --------> equation B

Substitute equation B in equation A

`100\°=(arc\ FEH-[360\°-arc\ FEH])`

`100\°=2arc\ FEH-360\°`

`2arc\ FEH=360\°+100\°`

`arc\ FEH=230\°`

therefore

The answer is

The measure of arc FEH is equal to
`230\°`