step 1
Remember that, an equilateral triangle has three equal sides and three equal interior angles.
The measure of each interior angle is 60 degrees
In this problem the triangle BCD is an equilateral triangle
therefore
m< CBD=60 degrees
step 2
REmember that an isosceles triangle has two equal sides and two equal interior angles
In this problem, the triangle ABD is an isosceles triangle
therefore
mwe know that
The sum of the interior angles in any triangle must be equal to 180 degrees
so
62+62+mmm
step 3
Find the measure of angle ABC
we hve that
m by addition angle postulate
substitute the given values
mtherefore
the answer is
The angle ABC is 116 degrees