An equilateral triangle and an isosceles triangle share a common side. what is the measure of abc ?

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

Find the measure of the vertex angle ∠ABD of an isosceles triangle

we know that

An isosceles triangle has two equal sides and two equal angles

In this problem

----> the angles of the base are equals

Find the measure of the vertex angle ABD

------> the sum of the internal angles of a triangle is equal to 180 degrees

step 2

Find the measure of the angle  ∠CBD in the equilateral triangle

we know that

A equilateral triangle has three  equal sides and three equal angles

The measure of the internal angle in a equilateral triangle is equal to 60 degrees

so

step 3

Find the measure of the angle ∠ABC

we know that

---> by addition angle postulate

substitute the values