Question

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

Answer 1

Answer:

Part a) $m$

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) $arc\ GJI=180\°$

Step-by-step 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

$m$

$arc\ HG=80\°$ ----> by central angle

substitute

$m$

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

$arc\ GH=m$ ----> by central angle

so

$arc\ GH=80\°$

Part e) Measure of arc GJI

we know that

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