Question

Given that m 10 years ago

Answer 1

do you know which angle is <GHJ ?

Answer 2

yes @phi

Answer 3

Here is the picture

Answer 4

any idea what the angle <GHJ + < IHJ add up to ?
in the picture it's 154 + X (easier to type)

Answer 5

That's where I get confused, because there is no actual number for x.

Answer 6

it does not matter what the number is ... the idea is those two angles form a straight line
and a straight line is an angle of how many degrees?

Answer 7

Oh, I got x=26. I subtracted 154 from 180

Answer 8

yes.

we also know the two "marked angles" are equal (that is what the red arcs mean)
if we call them Y (for convenience)
the 3 angles of the triangle
Y+Y+X= 180
and also
from the first post
154+X= 180

so we can say
2Y+ X = 154+X
or (subtract off X from both sides)
2Y= 154

now you can find Y (i.e. angle HIJ)

Answer 9

I got y=77 degrees, thank you for all the help!!

Answer 10

or we could use x=26
and say
2Y+26= 180
2Y= 180-26
2Y= 154
Y= 77

Answer 11

the reasoning was a bit complicated... once people figured it out they said
let the < GHJ be called an "exterior angle"
and the exterior angle equals the sum of the two opposite angles.

that lets you write down
<GHJ = 2*<HIJ
or
154 = 2 * <HIJ
and <HIJ= 77

Answer 12

I posted a similar one just now, it's even harder. Your explanation makes sense, thank you again!