Question

In the circle below, f is the center, gi is the diameter and m

Answer 1

Part a)
`m<HIG=40\°`

Part b) IHG is a semicircle and GJI is a semicircle

Part c) HIJ is a major arc and HIJG is a major arc

Part d)
`arc\ GH=80\°`

Part e)
`arc\ GJI=180\°`

Explanation:

Part a) Give an inscribed angle

we know that

The inscribed angle measures half that of the arc comprising

so

in this problem m<HIG is an inscribed angle

`m<HIG=(1)/(2)(arc\ HG)`

`arc\ HG=80\°` ----> by central angle

substitute

`m<HIG=(1)/(2)(80\°)=40\°`

Part b) Give a semicircle

we know that

The diameter divide the circle into two semicircles

so

GI is a diameter

therefore

IHG is a semicircle

GJI is a semicircle

Part c) Give a major arc

we know that

The measure of a major arc is greater than 180 degrees

therefore

HIJ is a major arc

HIJG is a major arc

Part d) Measure of arc GH

we know that

`arc\ GH=m<HFG` ----> by central angle

so

`arc\ GH=80\°`

Part e) Measure of arc GJI

we know that

`arc\ GJI=180\°` ----> the arc represent a semicircle