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MATH / Central angles a,b, and c separate the circle into regions which are (1)/(3), (1)/(4), and (1)/(6) of the area of the circle respectively. How many degrees are there in central ang…

Problem

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

problem

Central angles aa,bb, and cc separate the circle into regions which are 13\frac{1}{3}, 14\frac{1}{4}, and 16\frac{1}{6} of the area of the circle respectively. How many degrees are there in central angle dd? [asy] draw(circle((0,0),1)); draw((0,0)--(1,0)); draw((0,0)--(0,1)); draw((0,0)--(1/2,-sqrt(3)/2)); draw((0,0)--(-sqrt(3)/2,-1/2)); label("bb",(0,0),NE); label("cc",(0,0),dir(-30)); label("dd",(0,0),dir(-100)); label("aa",(0,0),NW); [/asy]
Plain-text mathematical notation (without MathML)
Central angles a,b, and c separate the circle into regions which are (1)/(3), (1)/(4), and (1)/(6) of the area of the circle respectively. How many degrees are there in central angle d?

[asy]
draw(circle((0,0),1));
draw((0,0)--(1,0));
draw((0,0)--(0,1));
draw((0,0)--(1/2,-sqrt(3)/2));
draw((0,0)--(-sqrt(3)/2,-1/2));
label("b",(0,0),NE);
label("c",(0,0),dir(-30));
label("d",(0,0),dir(-100));
label("a",(0,0),NW);
[/asy]
Original LaTeX notation
Central angles $a$,$b$, and $c$ separate the circle into regions which are $\frac{1}{3}$, $\frac{1}{4}$, and $\frac{1}{6}$ of the area of the circle respectively. How many degrees are there in central angle $d$?

[asy]
draw(circle((0,0),1));
draw((0,0)--(1,0));
draw((0,0)--(0,1));
draw((0,0)--(1/2,-sqrt(3)/2));
draw((0,0)--(-sqrt(3)/2,-1/2));
label("$b$",(0,0),NE);
label("$c$",(0,0),dir(-30));
label("$d$",(0,0),dir(-100));
label("$a$",(0,0),NW);
[/asy]

level

Level 1

type

Prealgebra

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Source and history

task_id
ea0742c9-ec78-53fe-bcc0-f6f1b220ad3c
task_key
prealgebra--test--ea0742c9-ec78-53fe-bcc0-f6f1b220ad3c
task_revision_id
1
config / split
prealgebra / test

Official source

initial import