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MATH / Triangle ABC is an isosceles right triangle with a right angle at A. Segments BD and BE trisect angle ABC. What is the degree measure of angle BDE? [asy]draw((0,0)--(-1,0)--(-1,1)-…

Problem

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

problem

Triangle ABCABC is an isosceles right triangle with a right angle at AA. Segments BDBD and BEBE trisect angle ABCABC. What is the degree measure of angle BDEBDE? [asy]draw((0,0)--(-1,0)--(-1,1)--(0,0)--cycle,linewidth(2)); draw((0,0)--dir(165)*1/cos(pi/12),linewidth(2)); draw((0,0)--dir(150)*1/cos(pi/6),linewidth(2)); draw((-1,.07)--(-.93,.07)--(-.93,0),linewidth(1)); label("A",(-1,0),SW); label("B",(0,0),SE); label("C",(-1,1),NW); label("D",dir(150)*1/cos(pi/6),W); label("E",dir(165)*1/cos(pi/12),W); [/asy]
Plain-text mathematical notation (without MathML)
Triangle ABC is an isosceles right triangle with a right angle at A. Segments BD and BE trisect angle ABC. What is the degree measure of angle BDE?

[asy]draw((0,0)--(-1,0)--(-1,1)--(0,0)--cycle,linewidth(2));
draw((0,0)--dir(165)*1/cos(pi/12),linewidth(2));
draw((0,0)--dir(150)*1/cos(pi/6),linewidth(2));
draw((-1,.07)--(-.93,.07)--(-.93,0),linewidth(1));

label("A",(-1,0),SW);
label("B",(0,0),SE);
label("C",(-1,1),NW);
label("D",dir(150)*1/cos(pi/6),W);
label("E",dir(165)*1/cos(pi/12),W);
[/asy]
Original LaTeX notation
Triangle $ABC$ is an isosceles right triangle with a right angle at $A$. Segments $BD$ and $BE$ trisect angle $ABC$. What is the degree measure of angle $BDE$?

[asy]draw((0,0)--(-1,0)--(-1,1)--(0,0)--cycle,linewidth(2));
draw((0,0)--dir(165)*1/cos(pi/12),linewidth(2));
draw((0,0)--dir(150)*1/cos(pi/6),linewidth(2));
draw((-1,.07)--(-.93,.07)--(-.93,0),linewidth(1));

label("A",(-1,0),SW);
label("B",(0,0),SE);
label("C",(-1,1),NW);
label("D",dir(150)*1/cos(pi/6),W);
label("E",dir(165)*1/cos(pi/12),W);
[/asy]

level

Level 4

type

Prealgebra

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Source and history

task_id
aa049ce1-c4c2-555a-80e4-2f320eb56ffd
task_key
prealgebra--test--aa049ce1-c4c2-555a-80e4-2f320eb56ffd
task_revision_id
1
config / split
prealgebra / test

Official source

initial import