benchmarks.wiki

benchmarks.wiki / Public workspace

MATH / Rectangle WXYZ is drawn on △ABC, such that point W lies on segment AB, point X lies on segment AC, and points Y and Z lies on segment BC, as shown. If m∠BWZ=26^(∘) and m∠CXY=64^(∘)…

Problem

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

problem

Rectangle WXYZWXYZ is drawn on △ABC\triangle ABC, such that point WW lies on segment ABAB, point XX lies on segment ACAC, and points YY and ZZ lies on segment BCBC, as shown. If m∠BWZ=26∘m\angle BWZ=26^{\circ} and m∠CXY=64∘m\angle CXY=64^{\circ}, what is m∠BACm\angle BAC, in degrees? [asy] unitsize(0.3cm); draw((0,0)--(4.5,6)--(21,0)--cycle); draw((3,0)--(3,4)--(10,4)--(10,0)--cycle); label("B",(0,0),SW); label("W",(3,4),W); label("A",(4.5,6),N); label("X",(10,4),NE); label("C",(21,0),E); label("Y",(10,0),S); label("Z",(3,0),S); label(scale(0.7)*Label("26∘26^{\circ}",(2.4,2.6),S)); label(scale(0.8)*Label("64∘64^{\circ}",(11,3.5),S)); [/asy]
Plain-text mathematical notation (without MathML)
Rectangle WXYZ is drawn on △ABC, such that point W lies on segment AB, point X lies on segment AC, and points Y and Z lies on segment BC, as shown. If m∠BWZ=26^(∘) and m∠CXY=64^(∘), what is m∠BAC, in degrees? [asy]
unitsize(0.3cm);
draw((0,0)--(4.5,6)--(21,0)--cycle);
draw((3,0)--(3,4)--(10,4)--(10,0)--cycle);
label("B",(0,0),SW);
label("W",(3,4),W);
label("A",(4.5,6),N);
label("X",(10,4),NE);
label("C",(21,0),E);
label("Y",(10,0),S);
label("Z",(3,0),S);
label(scale(0.7)*Label("26^(∘)",(2.4,2.6),S));
label(scale(0.8)*Label("64^(∘)",(11,3.5),S));
[/asy]
Original LaTeX notation
Rectangle $WXYZ$ is drawn on $\triangle ABC$, such that point $W$ lies on segment $AB$, point $X$ lies on segment $AC$, and points $Y$ and $Z$ lies on segment $BC$, as shown. If $m\angle BWZ=26^{\circ}$ and $m\angle CXY=64^{\circ}$, what is $m\angle BAC$, in degrees? [asy]
unitsize(0.3cm);
draw((0,0)--(4.5,6)--(21,0)--cycle);
draw((3,0)--(3,4)--(10,4)--(10,0)--cycle);
label("B",(0,0),SW);
label("W",(3,4),W);
label("A",(4.5,6),N);
label("X",(10,4),NE);
label("C",(21,0),E);
label("Y",(10,0),S);
label("Z",(3,0),S);
label(scale(0.7)*Label("$26^{\circ}$",(2.4,2.6),S));
label(scale(0.8)*Label("$64^{\circ}$",(11,3.5),S));
[/asy]

level

Level 1

type

Geometry

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

task_id
0eb49bb5-dbd6-59da-8734-8f99d079914f
task_key
geometry--test--0eb49bb5-dbd6-59da-8734-8f99d079914f
task_revision_id
1
config / split
geometry / test

Official source

initial import