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MATH / The following diagonal is drawn in a regular heptagon, creating a pentagon and a…

Problem

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

problem

The following diagonal is drawn in a regular heptagon, creating a pentagon and a quadrilateral. What is the measure of xx, in degrees? Express your answer as a common fraction. [asy] import markers; for(int i=0; i <=7; ++i) { draw(dir(360*i/7+90)--dir(360*(i+1)/7+90)); } pair A = dir(360*0/7+90); pair F = dir(360*4/7+90); pair G = dir(360*5/7+90); pair H = dir(360*6/7+90); draw(A--F); markangle(Label("xx",Relative(0.5)),n=1,radius=18,G,F,A); [/asy]
Plain-text mathematical notation (without MathML)
The following diagonal is drawn in a regular heptagon, creating a pentagon and a quadrilateral.  What is the measure of x, in degrees?  Express your answer as a common fraction.

[asy]
import markers;
for(int i=0; i <=7; ++i) {
draw(dir(360*i/7+90)--dir(360*(i+1)/7+90));
}
pair A = dir(360*0/7+90);
pair F = dir(360*4/7+90);
pair G = dir(360*5/7+90);
pair H = dir(360*6/7+90);

draw(A--F);

markangle(Label("x",Relative(0.5)),n=1,radius=18,G,F,A);

[/asy]
Original LaTeX notation
The following diagonal is drawn in a regular heptagon, creating a pentagon and a quadrilateral.  What is the measure of $x$, in degrees?  Express your answer as a common fraction.

[asy]
import markers;
for(int i=0; i <=7; ++i) {
draw(dir(360*i/7+90)--dir(360*(i+1)/7+90));
}
pair A = dir(360*0/7+90);
pair F = dir(360*4/7+90);
pair G = dir(360*5/7+90);
pair H = dir(360*6/7+90);

draw(A--F);

markangle(Label("$x$",Relative(0.5)),n=1,radius=18,G,F,A);

[/asy]

level

Level 4

type

Geometry

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Source and history

task_id
541a5f23-26a9-5c49-85ce-20f0e9b7c78a
task_key
geometry--test--541a5f23-26a9-5c49-85ce-20f0e9b7c78a
task_revision_id
1
config / split
geometry / test

Official source

initial import