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[tex]\overline{AB}[/tex] and [tex]\overline{ED}[/tex] are parallel. What is the measure of [tex]\angle ABC[/tex]

A) [tex]45^\circ[/tex]
B) [tex]65^\circ[/tex]
C) [tex]55^\circ[/tex]
D) [tex]50^\circ[/tex]

texoverlineABtex and texoverlineEDtex are parallel What is the measure of texangle ABCtex A tex45circtex B tex65circtex C tex55circtex D tex50circtex class=

Respuesta :

Advent5647

Answer:

B: 65°

Step-by-step explanation:

Step 1:

AB ║ ED      Given

Step 2:

∠E = 65°      Given

Step 3:

∠ABC = 65°    Alt. Int. ∠'s   ( Alternate Interior ∠'s)

Answer:

B: 65°

Hope This Helps :)

dreaagd

[tex]\tt Step-by-step~explanation:[/tex]

To find the measure of ∠ABC, we need to know that the sum of the interior angles of a triangle is 180º.

[tex]\tt Step~1:[/tex]

Triangle CED has two given angles: 65º and 50º. We can add them together and subtract that from 180 to get the third measure.

[tex]\tt 65+50=115\\180-115=65[/tex]

[tex]\tt Step~2:[/tex]

Since lines AB and ED are parallel, that means m∠ACB is also 65º since the vertical angle is also 65º. Then, we can add 65 and 50 together and subtract that from 180 to get our answer.

[tex]\tt 65+50=115\\180-115=65[/tex]

[tex]\large\boxed{\tt Our~final~answer:~m\angle ABC=65~degrees }[/tex]

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