Equilateral triangle ABC and isosceles triangle DBC share side BC. If angle BDC= 34 and BD=BC, what is the measure of angle ABD?

I don't know how to solve this questions, can someone guide me through?

Start by drawing a diagram.

If BC=BD, then
∠BDC=∠BCD=34° (angles opposite equal sides.

Hence ∠CBD=180-(34+34)=112°
∠ABD=∠ABC+∠CBD=?

Recall that ΔABC is equilateral.

All angles in the equilateral triangle are 60°

In the isosceles triangle the two base angles are
73 ° each ......... ( (180-34)/2 )

so angle ABD = 60+73 or 133°

Go with MathMate, I misread the question

To solve this question, we can use the properties of isosceles triangles and the fact that angles in a triangle add up to 180 degrees.

First, let's label the angles in triangle ABC. Since it is an equilateral triangle, all of its angles are equal, so angle BAC = angle ABC = angle BCA.

Since angle DBC = 34 degrees, and BD=BC, it means that triangle BDC is an isosceles triangle. In an isosceles triangle, the base angles (the ones opposite the congruent sides) are equal.

Therefore, angle BCD = angle BDC = 34 degrees.

Since the angles in triangle BCD add up to 180 degrees, we can find the measure of angle CBD:

Angle CBD + angle BCD + angle BDC = 180 degrees

Let's substitute the known values:

Angle CBD + 34 degrees + 34 degrees = 180 degrees

Combine like terms:

Angle CBD + 68 degrees = 180 degrees

Now, isolate angle CBD:

Angle CBD = 180 degrees - 68 degrees

Angle CBD = 112 degrees

Since triangle ABC is equilateral, all its angles are equal, including angle BAC. Therefore, angle ABD is equal to:

Angle ABD = angle BAC = angle ABC = angle BCA

Since the sum of the angles in triangle ABC is 180 degrees, we can find the measure of angle ABD:

Angle ABD + angle BAC + angle ABC = 180 degrees

Let's substitute the known values:

Angle ABD + angle ABD + angle ABD = 180 degrees

Combine like terms:

3 * Angle ABD = 180 degrees

Now, isolate Angle ABD:

Angle ABD = 180 degrees / 3

Angle ABD = 60 degrees

Therefore, the measure of angle ABD is 60 degrees.