Answer: the measure of the indicated angle is 100 degrees
Explanation:
The sum of angles in a triangle is 180 degrees. Let x represent the unknown angle in the bigger triangle. Therefore,
x + 80 + 25 = 180 degrees
x + 105 = 180
x = 180 - 105 = 75 degrees.
Let z represent the other unknown angle in the smaller triangle. Since the sum of the angles on a straight line is 180 degrees, therefore
75 + 55 + z = 180
130 +z = 180
z = 180 - 130 = 50 degrees
Let y represent the unknown angle that we are looking for. Therefore,
50 + y + 30 = 180
80 + y = 180
y = 180 - 80 = 100 degrees