The three angles of every triangle add up to 180°, whatever the triangle looks like — long and thin or wide and flat. That one fact answers most triangle questions: add the angles you are given, then take the total from 180. An isosceles triangle adds a second fact — its two base angles are equal — so when you are given the angle at the top, subtract it from 180 and then HALVE what is left, because that amount belongs to two angles, not one.
Worked example
Problem In an isosceles triangle, the angle between the two equal sides is 40°. Find one of the two equal base angles.
The three angles add to 180°, and the two base angles are equal.
Take the given angle off first: 180 − 40 = 140.
That 140° is shared equally between the two base angles: 140 ÷ 2 = 70, so each is 70°.
Watch out Do not stop at the subtraction — 140° belongs to TWO angles, so it must still be halved.