Respuesta :

calculista

Answer:

Part a) [tex]m<HIG=40\°[/tex]

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) [tex]arc\ GH=80\°[/tex]

Part e) [tex]arc\ GJI=180\°[/tex]

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

[tex]m<HIG=\frac{1}{2}(arc\ HG)[/tex]

[tex]arc\ HG=80\°[/tex] ----> by central angle

substitute

[tex]m<HIG=\frac{1}{2}(80\°)=40\°[/tex]

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

[tex]arc\ GH=m<HFG[/tex] ----> by central angle

so

[tex]arc\ GH=80\°[/tex]

Part e) Measure of arc GJI

we know that

[tex]arc\ GJI=180\°[/tex] ----> the arc represent a semicircle

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