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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 angl…

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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] import olympiad; import geometry; size(150); defaultpen(linewidth(0.8)); draw((0,0)--(3,0)--(4,5)--(0,0)--(2,1.5)--(3,0)--(1.7,0.5)--(0,0)); label("PP", (1.7,0.5), S); label("QQ", (2,1.5), N); label("BB", (0,0),W); label("AA", (4,5), N); label("CC", (3,0), E); [/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]
import olympiad; import geometry; size(150); defaultpen(linewidth(0.8));
draw((0,0)--(3,0)--(4,5)--(0,0)--(2,1.5)--(3,0)--(1.7,0.5)--(0,0));
label("P", (1.7,0.5), S); label("Q", (2,1.5), N); label("B", (0,0),W); label("A", (4,5), N); label("C", (3,0), E);
[/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]
import olympiad; import geometry; size(150); defaultpen(linewidth(0.8));
draw((0,0)--(3,0)--(4,5)--(0,0)--(2,1.5)--(3,0)--(1.7,0.5)--(0,0));
label("$P$", (1.7,0.5), S); label("$Q$", (2,1.5), N); label("$B$", (0,0),W); label("$A$", (4,5), N); label("$C$", (3,0), E);
[/asy]

level

Level 5

type

Prealgebra

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Source and history

task_id
12e0fb9b-ed01-5b1c-afa0-f3b5e2fff82c
task_key
prealgebra--test--12e0fb9b-ed01-5b1c-afa0-f3b5e2fff82c
task_revision_id
1
config / split
prealgebra / test

Official source

initial import