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MATH / In the diagram shown here (which is not drawn to scale), suppose that △ABC∼△PAQ and △ABQ∼△QCP. If m∠BAC=70^(∘), then compute m∠PQC. [asy] size(150); defaultpen(linewidth(0.8)); pai…

Problem

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

problem

In the diagram shown here (which is not drawn to scale), suppose that △ABC∼△PAQ\triangle ABC \sim \triangle PAQ and △ABQ∼△QCP\triangle ABQ \sim \triangle QCP. If m∠BAC=70∘m\angle BAC = 70^\circ, then compute m∠PQCm\angle PQC. [asy] size(150); defaultpen(linewidth(0.8)); pair B = (0,0), C = (6,0), A = (2,4), Q = (1,0), P = (A + C)/2; draw(A--B--C--A--Q--P); label("BB",B,S); label("AA",A,N); label("CC",C,S); label("PP",P,E); label("QQ",Q,S); [/asy]
Plain-text mathematical notation (without MathML)
In the diagram shown here (which is not drawn to scale), suppose that △ABC∼△PAQ and △ABQ∼△QCP.  If m∠BAC=70^(∘), then compute m∠PQC. [asy]
size(150); defaultpen(linewidth(0.8));
pair B = (0,0), C = (6,0), A = (2,4), Q = (1,0), P = (A + C)/2;
draw(A--B--C--A--Q--P);
label("B",B,S); label("A",A,N); label("C",C,S); label("P",P,E); label("Q",Q,S);
[/asy]
Original LaTeX notation
In the diagram shown here (which is not drawn to scale), suppose that $\triangle ABC \sim \triangle PAQ$ and $\triangle ABQ \sim \triangle QCP$.  If $m\angle BAC = 70^\circ$, then compute $m\angle PQC$. [asy]
size(150); defaultpen(linewidth(0.8));
pair B = (0,0), C = (6,0), A = (2,4), Q = (1,0), P = (A + C)/2;
draw(A--B--C--A--Q--P);
label("$B$",B,S); label("$A$",A,N); label("$C$",C,S); label("$P$",P,E); label("$Q$",Q,S);
[/asy]

level

Level 5

type

Geometry

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Source and history

task_id
5836a068-387d-5b14-881b-9534c8f6c926
task_key
geometry--test--5836a068-387d-5b14-881b-9534c8f6c926
task_revision_id
1
config / split
geometry / test

Official source

initial import