Question

The sum of the measures of the remote interior angles of a triangle is half the measure of the angle adjacent to the exterior angle. find the measure of the exterior angle.

Answer 1

i'm not sure, but i think the answer is 60 degrees.

Answer 2

yes it actually is. how did you get it? :)

Answer 3

let remote angles = x and y
x + y = e
2(x+y) = 180-e
dividing
2 = 180 -e / e
solve this gives e = 60

Answer 4

let us assume the angle adjacent to the exterior measures x,
therefore, the sum of the remote interior angles will be 1/2x

according to the property,"the sum of the measuresof the angles of a triangle is always 180",
we get the following equation:
1/2x + X=180
2x + 1x/2=180
x= 180 * 2/3
x=120

but according to the equation, x is the angle adjacent to the exterior & it forms a linear pair with it.

so,
x + exterior angle =180
120 + exterior angle= 180
exterior angle=60