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MATH / In regular pentagon FGHIJ, extending the sides of the pentagon, as shown, forms a star. What is the measure of angle A in the figure? [asy] draw((-42.4,30.8)--(-10,30.8)--(0,63.2)-…

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Answer published by the source. Consult the official source to check your work against its answer.

problem

In regular pentagon FGHIJFGHIJ, extending the sides of the pentagon, as shown, forms a star. What is the measure of angle AA in the figure? [asy] draw((-42.4,30.8)--(-10,30.8)--(0,63.2)--(10,30.8)--(42.4,30.8)--(16.2,11.8)--(24.9,-18.1)--(0,0)--(-24.9,-18.1)--(-16.2,11.8)--cycle,linewidth(1)); draw((-10,30.8)--(10,30.8)--(16.2,11.8)--(0,0)--(-16.2,11.8)--cycle,linewidth(1)); label("AA",(-42.4,30.8),W); label("FF",(-10,30.8),NW); dot((-10,30.8)); label("GG",(10,30.8),NE); dot((10,30.8)); label("HH",(16.2,11.8),E); dot((16.2,11.8)); label("II",(0,0),S); dot((0,0)); label("JJ",(-16.2,11.8),WSW); dot((-16.2,11.8)); [/asy]
Plain-text mathematical notation (without MathML)
In regular pentagon FGHIJ, extending the sides of the pentagon, as shown, forms a star. What is the measure of angle A in the figure?

[asy]
draw((-42.4,30.8)--(-10,30.8)--(0,63.2)--(10,30.8)--(42.4,30.8)--(16.2,11.8)--(24.9,-18.1)--(0,0)--(-24.9,-18.1)--(-16.2,11.8)--cycle,linewidth(1));
draw((-10,30.8)--(10,30.8)--(16.2,11.8)--(0,0)--(-16.2,11.8)--cycle,linewidth(1));
label("A",(-42.4,30.8),W);
label("F",(-10,30.8),NW);
dot((-10,30.8));
label("G",(10,30.8),NE);
dot((10,30.8));
label("H",(16.2,11.8),E);
dot((16.2,11.8));
label("I",(0,0),S);
dot((0,0));
label("J",(-16.2,11.8),WSW);
dot((-16.2,11.8));
[/asy]
Original LaTeX notation
In regular pentagon $FGHIJ$, extending the sides of the pentagon, as shown, forms a star. What is the measure of angle $A$ in the figure?

[asy]
draw((-42.4,30.8)--(-10,30.8)--(0,63.2)--(10,30.8)--(42.4,30.8)--(16.2,11.8)--(24.9,-18.1)--(0,0)--(-24.9,-18.1)--(-16.2,11.8)--cycle,linewidth(1));
draw((-10,30.8)--(10,30.8)--(16.2,11.8)--(0,0)--(-16.2,11.8)--cycle,linewidth(1));
label("$A$",(-42.4,30.8),W);
label("$F$",(-10,30.8),NW);
dot((-10,30.8));
label("$G$",(10,30.8),NE);
dot((10,30.8));
label("$H$",(16.2,11.8),E);
dot((16.2,11.8));
label("$I$",(0,0),S);
dot((0,0));
label("$J$",(-16.2,11.8),WSW);
dot((-16.2,11.8));
[/asy]

level

Level 4

type

Prealgebra

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Source and history

task_id
7a521612-c575-5a29-aa60-88807a72c32d
task_key
prealgebra--test--7a521612-c575-5a29-aa60-88807a72c32d
task_revision_id
1
config / split
prealgebra / test

Official source

initial import