benchmarks.wiki

benchmarks.wiki / Public workspace

MATH / A regular pentagon and a regular hexagon are coplanar and share a common side…

Problem

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

problem

A regular pentagon and a regular hexagon are coplanar and share a common side AD¯\overline{AD}, as shown. What is the degree measure of angle BACBAC? [asy] draw((-10,0)--(10,0)--(20,17.3)--(10,34.6)--(-10,34.6)--(-20,17.3)--cycle,linewidth(1)); label("AA",(-10,0),SW); label("BB",(-20,17.3),W); label("DD",(10,0),SE); label("CC",(-16.2,19),ESE); draw((-10,0)--(-16.2,19)--(0,30.8)--(16.2,19)--(10,0),linewidth(1)); [/asy]
Plain-text mathematical notation (without MathML)
A regular pentagon and a regular hexagon are coplanar and share a common side (AD)¯, as shown. What is the degree measure of angle BAC?

[asy]
draw((-10,0)--(10,0)--(20,17.3)--(10,34.6)--(-10,34.6)--(-20,17.3)--cycle,linewidth(1));
label("A",(-10,0),SW);
label("B",(-20,17.3),W);
label("D",(10,0),SE);
label("C",(-16.2,19),ESE);
draw((-10,0)--(-16.2,19)--(0,30.8)--(16.2,19)--(10,0),linewidth(1));
[/asy]
Original LaTeX notation
A regular pentagon and a regular hexagon are coplanar and share a common side $\overline{AD}$, as shown. What is the degree measure of angle $BAC$?

[asy]
draw((-10,0)--(10,0)--(20,17.3)--(10,34.6)--(-10,34.6)--(-20,17.3)--cycle,linewidth(1));
label("$A$",(-10,0),SW);
label("$B$",(-20,17.3),W);
label("$D$",(10,0),SE);
label("$C$",(-16.2,19),ESE);
draw((-10,0)--(-16.2,19)--(0,30.8)--(16.2,19)--(10,0),linewidth(1));
[/asy]

level

Level 4

type

Prealgebra

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
c64d3178-dfbc-5cb0-a1e2-0d829ca97ef6
task_key
prealgebra--test--c64d3178-dfbc-5cb0-a1e2-0d829ca97ef6
task_revision_id
1
config / split
prealgebra / test

Official source

initial import