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MATH / In the diagram, the centre of the circle is O. The area of the shaded region is 20% of the area of the circle. What is the value of x? [asy] filldraw(Circle((0,0),1),gray(0.8),line…

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problem

In the diagram, the centre of the circle is O.O. The area of the shaded region is 20%20\% of the area of the circle. What is the value of $x?$ [asy] filldraw(Circle((0,0),1),gray(0.8),linewidth(1)); filldraw((cos(pi/5),sin(pi/5))--(0,0)--(cos(-pi/5),sin(-pi/5))..(-1,0)..cycle,white,linewidth(1)); label("OO", (0,0), W); label("x∘x^\circ", (0.1,0), E); [/asy]
Plain-text mathematical notation (without MathML)
In the diagram, the centre of the circle is O. The area of the shaded region is 20% of the area of the circle. What is the value of $x?$ [asy]
filldraw(Circle((0,0),1),gray(0.8),linewidth(1));
filldraw((cos(pi/5),sin(pi/5))--(0,0)--(cos(-pi/5),sin(-pi/5))..(-1,0)..cycle,white,linewidth(1));
label("O", (0,0), W);
label("x^(∘)", (0.1,0), E);
[/asy]
Original LaTeX notation
In the diagram, the centre of the circle is $O.$ The area of the shaded region is $20\%$ of the area of the circle. What is the value of $x?$ [asy]
filldraw(Circle((0,0),1),gray(0.8),linewidth(1));
filldraw((cos(pi/5),sin(pi/5))--(0,0)--(cos(-pi/5),sin(-pi/5))..(-1,0)..cycle,white,linewidth(1));
label("$O$", (0,0), W);
label("$x^\circ$", (0.1,0), E);
[/asy]

level

Level 1

type

Geometry

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Source and history

task_id
6fb7501f-9262-5ee8-8d4b-2eac90de1934
task_key
geometry--test--6fb7501f-9262-5ee8-8d4b-2eac90de1934
task_revision_id
1
config / split
geometry / test

Official source

initial import