1) Prove that the base angles of an isosceles triangle are acute angles.
2) Find the measures of an isosceles triangle if the base angle is twice bigger than the vertex angle.

Question

1) Prove that the base angles of an isosceles triangle are acute angles.
2) Find the measures of an isosceles triangle if the base angle is twice bigger than the vertex angle.

rulnick · Answer

isosceles implies two base angles are identical
call their measures x
sum of base angles is 2x
sum of all three angles is 180
call third angle's measure y
2x + y  = 180
2x = 180 - y
but y>0
so 2x < 180
x < 90

anonymous · Answer

1. all three angles in a triangle is 180.  in a isoleces the base angles equal each other.  

i agree with rulnick

rulnick · Answer

For #2, x+2x+2x = 180
5x = 180
x= 36
36, 72, 72 is the ans (degrees)

anonymous · Answer

how about if the base angle is three times smaller than its exterior angle

rulnick · Answer

then the base angle would have to be 90, which is impossible for isosceles

anonymous · Answer

ok, thank you so much