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
∠ABD=∠BAD=
----> 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\°](https://tex.z-dn.net/?f=180%5C%C2%B0)
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 ![60\°](https://tex.z-dn.net/?f=60%5C%C2%B0)
so
∠CBD=![60\°](https://tex.z-dn.net/?f=60%5C%C2%B0)
Step 3
Find the measure of the angle ∠ABC
∠ABC=∠ABD+∠DBC
substitute the values
∠ABC=![48\°+66\°=114\°](https://tex.z-dn.net/?f=48%5C%C2%B0%2B66%5C%C2%B0%3D114%5C%C2%B0)
therefore
<u>the answer is</u>
the measure of the angle ∠ABC is ![114\°](https://tex.z-dn.net/?f=114%5C%C2%B0)