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MATH / In the figure, BA=AD=DC and point D is on segment BC. The measure of angle ACD is 22.5 degrees. What is the measure of angle ABC? [asy] import olympiad; import geometry; size(150);…

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problem

In the figure, BA=AD=DCBA = AD = DC and point DD is on segment BCBC. The measure of angle ACDACD is 22.5 degrees. What is the measure of angle ABCABC? [asy] import olympiad; import geometry; size(150); defaultpen(linewidth(0.8)); draw((0,0)--(6+3*sqrt(2),0)--(3,3)--cycle); draw((3,3)--(6,0)); label("BB",(0,0),W); label("AA",(3,3),N); label("CC",(6+3*sqrt(2),0),E); label("DD",(6,0),S); [/asy]
Plain-text mathematical notation (without MathML)
In the figure, BA=AD=DC and point D is on segment BC. The measure of angle ACD is 22.5 degrees. What is the measure of angle ABC? [asy]
import olympiad; import geometry; size(150); defaultpen(linewidth(0.8));
draw((0,0)--(6+3*sqrt(2),0)--(3,3)--cycle);
draw((3,3)--(6,0));
label("B",(0,0),W); label("A",(3,3),N); label("C",(6+3*sqrt(2),0),E); label("D",(6,0),S);
[/asy]
Original LaTeX notation
In the figure, $BA = AD = DC$ and point $D$ is on segment $BC$. The measure of angle $ACD$ is 22.5 degrees. What is the measure of angle $ABC$? [asy]
import olympiad; import geometry; size(150); defaultpen(linewidth(0.8));
draw((0,0)--(6+3*sqrt(2),0)--(3,3)--cycle);
draw((3,3)--(6,0));
label("$B$",(0,0),W); label("$A$",(3,3),N); label("$C$",(6+3*sqrt(2),0),E); label("$D$",(6,0),S);
[/asy]

level

Level 2

type

Geometry

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Source and history

task_id
232ca5db-5837-5db2-b274-d37e0f371287
task_key
geometry--test--232ca5db-5837-5db2-b274-d37e0f371287
task_revision_id
1
config / split
geometry / test

Official source

initial import