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MATH / In quadrilateral ABCD, angle BAD and angle CDA are trisected as shown. What is the degree measure of angle AFD? [asy] size(150); pair A , B, C, D; A = (0,0); B = (2, 4); C = (7,4);…

Problem

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

problem

In quadrilateral ABCDABCD, angle BADBAD and angle CDACDA are trisected as shown. What is the degree measure of angle AFDAFD? [asy] size(150); pair A , B, C, D; A = (0,0); B = (2, 4); C = (7,4); D = (7, -2); draw( (0,0)--(2,4) -- (7,4) -- (7, -2)-- cycle); label("AA", A, SW); label("BB", B, NW); label("CC", C, NE); label("DD", D, SE); pair E, F; E = (4.5-.2,1-.2); F = (5, 3); draw(A--E--D); draw(A--F--D); label("EE", E, N); label("FF", F, NW); dot(A);dot(B);dot(C);dot(D);dot(E);dot(F); label("xx", (1, 1.5), S); label("xx", (2, 1), S+W); label("xx", (2, -1), N+N+N+W); label("yy", (5.5+.3, .5-.3), S); label("yy", (6.5+.3, 0)); label("yy", (5+.5, -1.5+.3)); label("110∘110^{\circ}",(2.5,3.5)); label("100∘100^{\circ}",(6.5-.2,3.5)); [/asy]
Plain-text mathematical notation (without MathML)
In quadrilateral ABCD, angle BAD and angle CDA are trisected as shown. What is the degree measure of angle AFD?

[asy]
size(150);
pair A , B, C, D; A = (0,0); B = (2, 4); C = (7,4); D = (7, -2);
draw( (0,0)--(2,4) -- (7,4) -- (7, -2)-- cycle);
label("A", A, SW);
label("B", B, NW);
label("C", C, NE);
label("D", D, SE);
pair E, F;
E = (4.5-.2,1-.2); F = (5, 3);
draw(A--E--D); draw(A--F--D);
label("E", E, N); label("F", F, NW);
dot(A);dot(B);dot(C);dot(D);dot(E);dot(F);
label("x", (1, 1.5), S); label("x", (2, 1), S+W); label("x", (2, -1), N+N+N+W);
label("y", (5.5+.3, .5-.3), S); label("y", (6.5+.3, 0)); label("y", (5+.5, -1.5+.3));
label("110^(∘)",(2.5,3.5)); label("100^(∘)",(6.5-.2,3.5));
[/asy]
Original LaTeX notation
In quadrilateral $ABCD$, angle $BAD$ and angle $CDA$ are trisected as shown. What is the degree measure of angle $AFD$?

[asy]
size(150);
pair A , B, C, D; A = (0,0); B = (2, 4); C = (7,4); D = (7, -2);
draw( (0,0)--(2,4) -- (7,4) -- (7, -2)-- cycle);
label("$A$", A, SW);
label("$B$", B, NW);
label("$C$", C, NE);
label("$D$", D, SE);
pair E, F;
E = (4.5-.2,1-.2); F = (5, 3);
draw(A--E--D); draw(A--F--D);
label("$E$", E, N); label("$F$", F, NW);
dot(A);dot(B);dot(C);dot(D);dot(E);dot(F);
label("$x$", (1, 1.5), S); label("$x$", (2, 1), S+W); label("$x$", (2, -1), N+N+N+W);
label("$y$", (5.5+.3, .5-.3), S); label("$y$", (6.5+.3, 0)); label("$y$", (5+.5, -1.5+.3));
label("$110^{\circ}$",(2.5,3.5)); label("$100^{\circ}$",(6.5-.2,3.5));
[/asy]

level

Level 5

type

Prealgebra

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Source and history

task_id
1d18a521-2d7e-5a5c-881d-a4f725f1f0cf
task_key
prealgebra--test--1d18a521-2d7e-5a5c-881d-a4f725f1f0cf
task_revision_id
1
config / split
prealgebra / test

Official source

initial import