Question

In isosceles triangle △ABC, AC is the base and AD is the angle bisector of ∠A. What are the measures of the angles of this triangle if m∠ADB=110°?

I have also tried 220/3 as the base angle, but that is incorrect. Thank you!

Answer 1

Explanation: The triangle is isosceles, meaning it has two twin sides, that make two twin angles, namely AB = BC, and the angles at A and C are twins as well.

now, the AD segment, is an angle bisector, meaning it cuts the angle at A in two equal halves, so if say the angles are x° each, then the bisectors cut it in (x/2)°.

now, we know ∡ADB is 110°, therefore its supplementary angle, in green, is 70°.

recall that the sum of all interior angles in a triangle is 180°, thus Check out the photo below