Use the properties of exterior angles of triangles to find angle b.

Answer 1

To find angle b, we need to use the properties of exterior angles of a triangle.

The sum of the exterior angles of any polygon is always 360 degrees.

In a triangle, the sum of the measures of the three exterior angles equals 360 degrees.

Therefore, we can set up the equation:

angle b + angle c + angle a = 360 degrees

Given that angle a = 110 degrees and angle c = 75 degrees, substituting these values in the equation, we get:

angle b + 75 degrees + 110 degrees = 360 degrees

Combining like terms:

angle b + 185 degrees = 360 degrees

Now, we can solve for angle b by subtracting 185 degrees from both sides of the equation:

angle b = 360 degrees - 185 degrees

angle b = 175 degrees

Therefore, the measure of angle b is 175 degrees.