Question

In the figure below, CEF is an equilateral triangle. Points B, C and E are collinear; Points A, C and F are collinear; g = 40 degrees; and k = 45 degrees. Find angle j.

Answer 1

http://static.k12.com/eli/ecollege/941/1_54810/2_45713_6_54837/83a3d06953122daaf3dd7fdaddd22cc8bb814086/media/56fb729a3d296d9b0a6488262cfcff227007e30f/mediaasset_1357738_1.jpg

Answer 2

75
105
60
45

Answer 3

@jim_thompson5910

Answer 4

CEF is an equilateral triangle, so that means all three sides of CEF are congruent

also, all three angles of CEF are congruent

Answer 5

what is the measure of each angle in triangle CEF?

Answer 6

idk

Answer 7

CEF is equilateral, so we know all three angles of CEF are congruent

that means

m = L = n

also

m+L+n = 180

m+m+m = 180

3m = 180

m = 60

each angle is equal to 60

Answer 8

so i add 60

Answer 9

thats part of it

Answer 10

what is the measure of angle i ?

Answer 11

hint: angle i and angle L are vertical angles

Answer 12

60

Answer 13

good

Answer 14

since B, C, E are collinear, ie they fall on the same line

this means i+j+k = 180

the three angles form a straight angle (aka a straight line)

Answer 15

we know

i = 60
k = 45

plug them into i+j+k = 180 and solve for j

Answer 16

ok

Answer 17

i got 105

Answer 18

60+45 = 105

Answer 19

so you should have 105+j = 180

Answer 20

you haven't fully isolated j yet though

Answer 21

i got 75

Answer 22

j = 75 is the answer