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°?

Isosceles triangle:

* two sides are equal.

* the base angle are always equal and

* the altitude is a perpendicular distance from the vertex to the base.

Since, the triangle ABC is an isosceles and AC is the base

⇒ AB=BC and  

Also, AD is the angle bisector of , which implies that it cuts the angle at A in two equal halves,

let , then the bisectors cuts it in .

As per the given information, we know  is 110°, therefore, the line BDC forms a supplementary angle;

⇒

As shown in picture given below:

By sum of all interior angles in a triangle is 180 degree, thus

or

Simplify:

Therefore, the .

Now, to find the angle B, we have;

   [Sum of the measure of the angles in a triangle is 180 degree]

or

 or

Simplify:

.

the solution is 12x-6y