Answer:
The measure of angle ABC is 50°
Explanation:
step 1
Find the measure of angle ACB
we know that
∠ACB+∠ACD=180° ----> by supplementary angles
see the attached figure to better understand the problem
∠ACB=180°-127°=53°
step 2
Find the measure of angle ABC
we know that
The sum of the interior angles of a triangle must be equal to 180 degrees
so
∠ABC+∠ACB+∠BAC=180°
substitute the given values
∠ABC+53°+77°=180°
∠ABC=180°-130°=50°