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MATH / In the circle with center O and diameters AC and BD, the angle AOD measures 54 degrees. What is the measure, in degrees, of angle AOB? [asy] draw(circle((0,0),1)); label("O",(0,0),…

Problem

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

problem

In the circle with center OO and diameters ACAC and BDBD, the angle AODAOD measures 5454 degrees. What is the measure, in degrees, of angle AOBAOB? [asy] draw(circle((0,0),1)); label("O",(0,0),SE); draw((-1,0)--(1,0)); draw((0.5877852522924731291,0.80901699437)--(-0.5877852522924731291,-0.80901699437)); label("B",(-1,0),W); label("D",(1,0),E); label("A",(0.5877852522924731291,0.80901699437),NE); label("C",(-0.5877852522924731291,-0.80901699437),SW); dot((0,0)); dot((-0.5877852522924731291,-0.80901699437)); dot((0.5877852522924731291,0.80901699437)); dot((-1,0)); dot((1,0)); [/asy]
Plain-text mathematical notation (without MathML)
In the circle with center O and diameters AC and BD, the angle AOD measures 54 degrees. What is the measure, in degrees, of angle AOB? [asy]
draw(circle((0,0),1));
label("O",(0,0),SE);
draw((-1,0)--(1,0));
draw((0.5877852522924731291,0.80901699437)--(-0.5877852522924731291,-0.80901699437));
label("B",(-1,0),W);
label("D",(1,0),E);
label("A",(0.5877852522924731291,0.80901699437),NE);
label("C",(-0.5877852522924731291,-0.80901699437),SW);
dot((0,0));
dot((-0.5877852522924731291,-0.80901699437));
dot((0.5877852522924731291,0.80901699437));
dot((-1,0));
dot((1,0));
[/asy]
Original LaTeX notation
In the circle with center $O$ and diameters $AC$ and $BD$, the angle $AOD$ measures $54$ degrees. What is the measure, in degrees, of angle $AOB$? [asy]
draw(circle((0,0),1));
label("O",(0,0),SE);
draw((-1,0)--(1,0));
draw((0.5877852522924731291,0.80901699437)--(-0.5877852522924731291,-0.80901699437));
label("B",(-1,0),W);
label("D",(1,0),E);
label("A",(0.5877852522924731291,0.80901699437),NE);
label("C",(-0.5877852522924731291,-0.80901699437),SW);
dot((0,0));
dot((-0.5877852522924731291,-0.80901699437));
dot((0.5877852522924731291,0.80901699437));
dot((-1,0));
dot((1,0));
[/asy]

level

Level 1

type

Geometry

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Source and history

task_id
fb553605-abf4-56e7-8b4a-cc220474151e
task_key
geometry--test--fb553605-abf4-56e7-8b4a-cc220474151e
task_revision_id
1
config / split
geometry / test

Official source

initial import