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MATH / In circle O, (PN)¯ and (GA)¯ are diameters and m∠GOP=78^(∘). How many degrees are in the measure of ∠NGA? [asy] draw((0,1)..(1,0)..(0,-1)..(-1,0)..cycle); draw((.777,.629)--(-.777,…

Problem

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

problem

In circle OO, PN¯\overline{PN} and GA¯\overline{GA} are diameters and m∠GOP=78∘\angle GOP=78^\circ. How many degrees are in the measure of ∠NGA\angle NGA? [asy] draw((0,1)..(1,0)..(0,-1)..(-1,0)..cycle); draw((.777,.629)--(-.777,-.629)); draw((-.777,.629)--(.777,-.629)); draw((.777,.629)--(-.777,.629)); label("OO",(0,0),S); label("NN",(.777,.629),NE); label("AA",(.777,-.629),SE); label("PP",(-.777,-.629),SW); label("GG",(-.777,.629),NW); label("78∘78^\circ",(0,0),2W); [/asy]
Plain-text mathematical notation (without MathML)
In circle O, (PN)¯ and (GA)¯ are diameters and m∠GOP=78^(∘). How many degrees are in the measure of ∠NGA? [asy]
draw((0,1)..(1,0)..(0,-1)..(-1,0)..cycle);
draw((.777,.629)--(-.777,-.629));
draw((-.777,.629)--(.777,-.629));
draw((.777,.629)--(-.777,.629));
label("O",(0,0),S);
label("N",(.777,.629),NE);
label("A",(.777,-.629),SE);
label("P",(-.777,-.629),SW);
label("G",(-.777,.629),NW);
label("78^(∘)",(0,0),2W);
[/asy]
Original LaTeX notation
In circle $O$, $\overline{PN}$ and $\overline{GA}$ are diameters and m$\angle GOP=78^\circ$. How many degrees are in the measure of $\angle NGA$? [asy]
draw((0,1)..(1,0)..(0,-1)..(-1,0)..cycle);
draw((.777,.629)--(-.777,-.629));
draw((-.777,.629)--(.777,-.629));
draw((.777,.629)--(-.777,.629));
label("$O$",(0,0),S);
label("$N$",(.777,.629),NE);
label("$A$",(.777,-.629),SE);
label("$P$",(-.777,-.629),SW);
label("$G$",(-.777,.629),NW);
label("$78^\circ$",(0,0),2W);
[/asy]

level

Level 2

type

Geometry

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Source and history

task_id
bbffef23-27b5-55ac-b14e-58508347cd0d
task_key
geometry--test--bbffef23-27b5-55ac-b14e-58508347cd0d
task_revision_id
1
config / split
geometry / test

Official source

initial import