DOE
contains points D (2,3)
, O (0,0)
, and E (5,1)
. Which of the following angles are both adjacent and supplementary to ∠DOE
?(1 point)
3 answers
There are no options provided, so we cannot determine which angles are both adjacent and supplementary to ∠DOE.
∠DOE
contains points D (2,3)
, O (0,0)
, and E (5,1)
. Which of the following angles are both adjacent and supplementary to ∠DOE
?(1 point)
Responses
∠DOF
, with F (10,2)
∠DOF
, with F open paren 10 comma 2 close paren
∠DOF
, with F(−2,−3)
∠DOF
, with F open paren negative 2 comma negative 3 close paren
∠DOF
, with F(−5,−1)
∠DOF
, with F open paren negative 5 comma negative 1 close paren
∠EOF
, with F(−5,−1)
∠EOF
, with F open paren negative 5 comma negative 1 close paren
∠EOF
, with F(−2,−3)
∠EOF
, with F open paren negative 2 comma negative 3 close paren
∠EOF
, with F(10,2)
contains points D (2,3)
, O (0,0)
, and E (5,1)
. Which of the following angles are both adjacent and supplementary to ∠DOE
?(1 point)
Responses
∠DOF
, with F (10,2)
∠DOF
, with F open paren 10 comma 2 close paren
∠DOF
, with F(−2,−3)
∠DOF
, with F open paren negative 2 comma negative 3 close paren
∠DOF
, with F(−5,−1)
∠DOF
, with F open paren negative 5 comma negative 1 close paren
∠EOF
, with F(−5,−1)
∠EOF
, with F open paren negative 5 comma negative 1 close paren
∠EOF
, with F(−2,−3)
∠EOF
, with F open paren negative 2 comma negative 3 close paren
∠EOF
, with F(10,2)
To find angles that are both adjacent and supplementary to ∠DOE, we need to find angles that share a side with ∠DOE and add up to 180 degrees.
Let's calculate the slope of line DE:
m(DE) = (1 - 3) / (5 - 2) = -2/3
The slope of the line DE helps us determine the slopes of lines that are adjacent to ∠DOE.
Option ∠DOF with F(10,2):
m(DF) = (2 - 3) / (10 - 2) = -1/8
Since -2/3 * -1/8 = 1/12, the slopes are not negative reciprocals, so ∠DOF is not adjacent and supplementary to ∠DOE.
Option ∠DOF with F(-2,-3):
m(DF) = (-3 - 3) / (-2 - 2) = -3/4
Since -2/3 * -3/4 = 1/2, the slopes are negative reciprocals, so ∠DOF is adjacent and supplementary to ∠DOE.
Option ∠DOF with F(-5,-1):
m(DF) = (-1 - 3) / (-5 - 2) = 4/7
Since -2/3 * 4/7 = -8/21, the slopes are not negative reciprocals, so ∠DOF is not adjacent and supplementary to ∠DOE.
Option ∠EOF with F(-5,-1):
m(EF) = (-1 - 1) / (-5 - 5) = -2/10 = -1/5
Since -2/3 * -1/5 = 2/15, the slopes are not negative reciprocals, so ∠EOF is not adjacent and supplementary to ∠DOE.
Option ∠EOF with F(-2,-3):
m(EF) = (-3 - 1) / (-2 - 5) = -4/7
Since -2/3 * -4/7 = 8/21, the slopes are not negative reciprocals, so ∠EOF is not adjacent and supplementary to ∠DOE.
Option ∠EOF with F(10,2):
m(EF) = (2 - 1) / (10 - 5) = 1/5
Since -2/3 * 1/5 = -2/15, the slopes are not negative reciprocals, so ∠EOF is not adjacent and supplementary to ∠DOE.
Therefore, the only angle that is both adjacent and supplementary to ∠DOE is ∠DOF with F(-2,-3).
Let's calculate the slope of line DE:
m(DE) = (1 - 3) / (5 - 2) = -2/3
The slope of the line DE helps us determine the slopes of lines that are adjacent to ∠DOE.
Option ∠DOF with F(10,2):
m(DF) = (2 - 3) / (10 - 2) = -1/8
Since -2/3 * -1/8 = 1/12, the slopes are not negative reciprocals, so ∠DOF is not adjacent and supplementary to ∠DOE.
Option ∠DOF with F(-2,-3):
m(DF) = (-3 - 3) / (-2 - 2) = -3/4
Since -2/3 * -3/4 = 1/2, the slopes are negative reciprocals, so ∠DOF is adjacent and supplementary to ∠DOE.
Option ∠DOF with F(-5,-1):
m(DF) = (-1 - 3) / (-5 - 2) = 4/7
Since -2/3 * 4/7 = -8/21, the slopes are not negative reciprocals, so ∠DOF is not adjacent and supplementary to ∠DOE.
Option ∠EOF with F(-5,-1):
m(EF) = (-1 - 1) / (-5 - 5) = -2/10 = -1/5
Since -2/3 * -1/5 = 2/15, the slopes are not negative reciprocals, so ∠EOF is not adjacent and supplementary to ∠DOE.
Option ∠EOF with F(-2,-3):
m(EF) = (-3 - 1) / (-2 - 5) = -4/7
Since -2/3 * -4/7 = 8/21, the slopes are not negative reciprocals, so ∠EOF is not adjacent and supplementary to ∠DOE.
Option ∠EOF with F(10,2):
m(EF) = (2 - 1) / (10 - 5) = 1/5
Since -2/3 * 1/5 = -2/15, the slopes are not negative reciprocals, so ∠EOF is not adjacent and supplementary to ∠DOE.
Therefore, the only angle that is both adjacent and supplementary to ∠DOE is ∠DOF with F(-2,-3).
3 answers