benchmarks.wiki

benchmarks.wiki / Public workspace

MATH / The trisectors of angles B and C of scalene triangle ABC meet at points P and Q, as shown. Angle A measures 39 degrees and angle QBP measures 14 degrees. What is the measure of ang…

Problem

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

problem

The trisectors of angles BB and CC of scalene triangle ABCABC meet at points PP and QQ, as shown. Angle AA measures 39 degrees and angle QBPQBP measures 14 degrees. What is the measure of angle BPCBPC? [asy]unitsize(2cm); label("BB",(0,0),W); label("AA",(1.2,1.5),N); label("CC",(1,0),E); label("QQ",(.8,.6),N); label("PP",(.7,.2),N); draw((0,0)--(1.2,1.5)--(1,0)--cycle,linewidth(1)); draw((0,0)--(.8,.6)--(1,0),linewidth(1)); draw((0,0)--(.7,.2)--(1,0),linewidth(1)); [/asy]
Plain-text mathematical notation (without MathML)
The trisectors of angles B and C of scalene triangle ABC meet at points P and Q, as shown. Angle A measures 39 degrees and angle QBP measures 14 degrees. What is the measure of angle BPC?

[asy]unitsize(2cm);
label("B",(0,0),W);

label("A",(1.2,1.5),N);
label("C",(1,0),E);
label("Q",(.8,.6),N);
label("P",(.7,.2),N);

draw((0,0)--(1.2,1.5)--(1,0)--cycle,linewidth(1));
draw((0,0)--(.8,.6)--(1,0),linewidth(1));
draw((0,0)--(.7,.2)--(1,0),linewidth(1));
[/asy]
Original LaTeX notation
The trisectors of angles $B$ and $C$ of scalene triangle $ABC$ meet at points $P$ and $Q$, as shown. Angle $A$ measures 39 degrees and angle $QBP$ measures 14 degrees. What is the measure of angle $BPC$?

[asy]unitsize(2cm);
label("$B$",(0,0),W);

label("$A$",(1.2,1.5),N);
label("$C$",(1,0),E);
label("$Q$",(.8,.6),N);
label("$P$",(.7,.2),N);

draw((0,0)--(1.2,1.5)--(1,0)--cycle,linewidth(1));
draw((0,0)--(.8,.6)--(1,0),linewidth(1));
draw((0,0)--(.7,.2)--(1,0),linewidth(1));
[/asy]

level

Level 5

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
34fe14e7-4149-542e-8497-2591caa1f2a6
task_key
prealgebra--test--34fe14e7-4149-542e-8497-2591caa1f2a6
task_revision_id
1
config / split
prealgebra / test

Official source

initial import