benchmarks.wiki

benchmarks.wiki / Public workspace

MATH / Triangles BDC and ACD are coplanar and isosceles. If we have m∠ABC=70^(∘), what is m∠BAC, in degrees? [asy] unitsize(2 cm); defaultpen(linewidth(1pt)+fontsize(10pt)); pair a,b,c,d;…

Problem

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

problem

Triangles BDCBDC and ACDACD are coplanar and isosceles. If we have m∠ABC=70∘m\angle ABC = 70^\circ, what is m∠BACm\angle BAC, in degrees? [asy] unitsize(2 cm); defaultpen(linewidth(1pt)+fontsize(10pt)); pair a,b,c,d; b = (0,0); c = (1,0); d = c+dir(140); a = d+dir(70); draw(a--b--c--cycle); draw(d--c); pair s,t; s = (.5,0)+(0,.05); t = (.5,0)+(0,-.05); draw(s--t); s = .5*(c+d) + .05*dir(50); t = .5*(c+d) - .05*dir(50); draw(s--t); s = .5*(a+d) + .05*dir(160); t = .5*(a+d) - .05*dir(160); draw(s--t); label("A",a,N); label("B",b,SW); label("C",c,SE); label("D",d,NW); label("70∘70^\circ",b+(.05,.03),NE); [/asy]
Plain-text mathematical notation (without MathML)
Triangles BDC and ACD are coplanar and isosceles. If we have m∠ABC=70^(∘), what is m∠BAC, in degrees?

[asy]
unitsize(2 cm);

defaultpen(linewidth(1pt)+fontsize(10pt));
pair a,b,c,d;
b = (0,0);
c = (1,0);
d = c+dir(140);
a = d+dir(70);
draw(a--b--c--cycle);
draw(d--c);
pair s,t;
s = (.5,0)+(0,.05);
t = (.5,0)+(0,-.05);
draw(s--t);
s = .5*(c+d) + .05*dir(50);
t = .5*(c+d) - .05*dir(50);
draw(s--t);
s = .5*(a+d) + .05*dir(160);
t = .5*(a+d) - .05*dir(160);
draw(s--t);
label("A",a,N);
label("B",b,SW);
label("C",c,SE);
label("D",d,NW);
label("70^(∘)",b+(.05,.03),NE);
[/asy]
Original LaTeX notation
Triangles $BDC$ and $ACD$ are coplanar and isosceles. If we have $m\angle ABC = 70^\circ$, what is $m\angle BAC$, in degrees?

[asy]
unitsize(2 cm);

defaultpen(linewidth(1pt)+fontsize(10pt));
pair a,b,c,d;
b = (0,0);
c = (1,0);
d = c+dir(140);
a = d+dir(70);
draw(a--b--c--cycle);
draw(d--c);
pair s,t;
s = (.5,0)+(0,.05);
t = (.5,0)+(0,-.05);
draw(s--t);
s = .5*(c+d) + .05*dir(50);
t = .5*(c+d) - .05*dir(50);
draw(s--t);
s = .5*(a+d) + .05*dir(160);
t = .5*(a+d) - .05*dir(160);
draw(s--t);
label("A",a,N);
label("B",b,SW);
label("C",c,SE);
label("D",d,NW);
label("$70^\circ$",b+(.05,.03),NE);
[/asy]

level

Level 2

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
c00aa723-1c78-5aa6-9e97-67f08ed3974d
task_key
geometry--test--c00aa723-1c78-5aa6-9e97-67f08ed3974d
task_revision_id
1
config / split
geometry / test

Official source

initial import