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MATH / In isosceles triangle ABC, if BC is extended to a point X such that AC=CX, what is the number of degrees in the measure of angle AXC? [asy] size(220); pair B, A = B + dir(40), C = …

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problem

In isosceles triangle ABCABC, if BCBC is extended to a point XX such that AC=CXAC = CX, what is the number of degrees in the measure of angle AXCAXC? [asy] size(220); pair B, A = B + dir(40), C = A + dir(-40), X = C + dir(0); draw(C--A--B--X--A); draw(A/2+.1*dir(-30)--A/2-.1*dir(-30)); draw((A+C)/2+.1*dir(30)--(A+C)/2-.1*dir(30)); label("A",A,N); label("C",C,S); label("B",B,S); label("X",X,S); label("30∘30^{\circ}",B+.1*dir(0),NE); draw(arc(B,1/3,0,40)); [/asy]
Plain-text mathematical notation (without MathML)
In isosceles triangle ABC, if BC is extended to a point X such that AC=CX, what is the number of degrees in the measure of angle AXC? [asy] size(220);
pair B, A = B + dir(40), C = A + dir(-40), X = C + dir(0);
draw(C--A--B--X--A); draw(A/2+.1*dir(-30)--A/2-.1*dir(-30));
draw((A+C)/2+.1*dir(30)--(A+C)/2-.1*dir(30));
label("A",A,N); label("C",C,S); label("B",B,S); label("X",X,S); label("30^(∘)",B+.1*dir(0),NE);
draw(arc(B,1/3,0,40));
[/asy]
Original LaTeX notation
In isosceles triangle $ABC$, if $BC$ is extended to a point $X$ such that $AC = CX$, what is the number of degrees in the measure of angle $AXC$? [asy] size(220);
pair B, A = B + dir(40), C = A + dir(-40), X = C + dir(0);
draw(C--A--B--X--A); draw(A/2+.1*dir(-30)--A/2-.1*dir(-30));
draw((A+C)/2+.1*dir(30)--(A+C)/2-.1*dir(30));
label("A",A,N); label("C",C,S); label("B",B,S); label("X",X,S); label("$30^{\circ}$",B+.1*dir(0),NE);
draw(arc(B,1/3,0,40));
[/asy]

level

Level 1

type

Geometry

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Source and history

task_id
21abfaf1-c55f-5718-a455-affd0de65598
task_key
geometry--test--21abfaf1-c55f-5718-a455-affd0de65598
task_revision_id
1
config / split
geometry / test

Official source

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