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MATH / Triangle ABC is a right triangle. If the measure of angle PAB is x^(∘) and the measure of angle ACB is expressed in the form (Mx+N)^(∘) with M=1, what is the value of M+N? [asy] dr…

Problem

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problem

Triangle ABCABC is a right triangle. If the measure of angle PABPAB is x∘x^\circ and the measure of angle ACBACB is expressed in the form (Mx+N)∘(Mx+N)^\circ with M=1M=1, what is the value of M+NM+N? [asy] draw((-10,0)--(20,0),linewidth(1),Arrows); draw((0,0)--(10,10/sqrt(3))--(10+10/3,0),linewidth(1)); draw((10,10/sqrt(3))+dir(-150)--(10,10/sqrt(3))+dir(-150)+dir(-60)--(10,10/sqrt(3))+dir(-60),linewidth(1)); dot((-3,0)); draw(dir(180)..dir(105)..dir(30),linewidth(1)); label("P",(-3,0),NW); label("A",(0,0),S); label("x∘x^\circ",(-1,1),N); label("B",(10,10/sqrt(3)),N); label("C",(10+10/3,0),NE); [/asy]
Plain-text mathematical notation (without MathML)
Triangle ABC is a right triangle. If the measure of angle PAB is x^(∘) and the measure of angle ACB is expressed in the form (Mx+N)^(∘) with M=1, what is the value of M+N?

[asy]
draw((-10,0)--(20,0),linewidth(1),Arrows);
draw((0,0)--(10,10/sqrt(3))--(10+10/3,0),linewidth(1));

draw((10,10/sqrt(3))+dir(-150)--(10,10/sqrt(3))+dir(-150)+dir(-60)--(10,10/sqrt(3))+dir(-60),linewidth(1));

dot((-3,0));

draw(dir(180)..dir(105)..dir(30),linewidth(1));

label("P",(-3,0),NW);
label("A",(0,0),S);
label("x^(∘)",(-1,1),N);
label("B",(10,10/sqrt(3)),N);
label("C",(10+10/3,0),NE);

[/asy]
Original LaTeX notation
Triangle $ABC$ is a right triangle. If the measure of angle $PAB$ is $x^\circ$ and the measure of angle $ACB$ is expressed in the form $(Mx+N)^\circ$ with $M=1$, what is the value of $M+N$?

[asy]
draw((-10,0)--(20,0),linewidth(1),Arrows);
draw((0,0)--(10,10/sqrt(3))--(10+10/3,0),linewidth(1));

draw((10,10/sqrt(3))+dir(-150)--(10,10/sqrt(3))+dir(-150)+dir(-60)--(10,10/sqrt(3))+dir(-60),linewidth(1));

dot((-3,0));

draw(dir(180)..dir(105)..dir(30),linewidth(1));

label("P",(-3,0),NW);
label("A",(0,0),S);
label("$x^\circ$",(-1,1),N);
label("B",(10,10/sqrt(3)),N);
label("C",(10+10/3,0),NE);

[/asy]

level

Level 5

type

Prealgebra

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Source and history

task_id
6d0d2b32-7ed2-59bf-9a77-c00f1b89c218
task_key
prealgebra--test--6d0d2b32-7ed2-59bf-9a77-c00f1b89c218
task_revision_id
1
config / split
prealgebra / test

Official source

initial import